A peregrine falcon is flying high over the gothic tower of the cathedral while elegant grey wagtails hop across the curving weir among flocks of gulls and geese. Is this really the worst city in the UK? Derby recently came bottom in a Which? poll of big UK cities for a short break. I’m only passing through on my way to the Peak District, but I plan to stop over on my way back. It’s certainly a useful hub for reaching the Peaks by bus or train.

Derbyshire has good public transport, a new unlimited bus ticket (£33 a week), and a growing number of local visitor attractions with incentives for car-free visitors. I’m hoping to put all these to the test during a week’s exploring.

Derby bus station is a 20-minute riverside stroll from the railway station under shady lime trees. I catch the Transpeak bus through Matlock and Bakewell to Ashford in the Water. On the 90-minute journey we pass yellow fields of buttercups, grazing sheep and steep green dales, all stitched together by miles of dry-stone wall. I’m travelling by bus as much for the top-deck views as the destinations themselves.

Approaching Ashford, we roll past the medieval Sheepwash Bridge, with the sunlit River Wye rippling through three low stone arches. When I return to the bridge on foot that evening, I see tufted ducks diving, and stippled brown trout swimming through the shadows. Nearby, villagers are taking down the decorative petals, seeds and leaves from this year’s well dressings.

I’m staying in the revamped Ashford Arms, which reopened a few months ago after a four-year closure and £1.6m refurbishment. It has a big beer garden and striking new decor: dark beams, ochre walls, watercolour landscapes and, in my room, a claw-footed freestanding bathtub (doubles from £90, B&B). Best of all, it’s opposite the bus stop, where services include one of the Peak District’s open-air sightseeing buses (day tickets £9.50/£5.50 concessions).

Trailing honeysuckle, wet elderflowers, mock orange blossom, fresh-cut hay: the passing countryside is full of summer smells next morning – one of many great things about open-topped buses. Swallows slice delicately through the air nearby. At Chatsworth, where I’m heading, car-free visitors get a free guidebook to the painted hall and richly panelled oak room, the gilded great stairs and tapestried bedchamber.

My favourite parts of the 105-acre (42-hectare) gardens are the wilder sections, where the trout stream runs through banks of orchids and pale starry camassia and a long coal tunnel leads under the hill to emerge in the rockery. As I get back on the Red route bus, the driver tells me to take the Blue route tomorrow (“worth it for the view from Winnats Pass alone”) and not to miss the chunky chips in the Ye Olde Nags Head in Castleton.

So next morning the other open-topper carries me through a roll call of iconic UK hiking places: Mam Tor, Stanage Edge, Hope Valley. When I step off at the Longshaw Estate, I spy a deer standing in the woods, staring. I walk past twisted mossy trees and purple rhododendrons. Green-walled lanes lead down through foxgloves and forget-me-nots, and rocky steps climb back up by the waterfalls of Padley Gorge to reach wide views across the moors (free).

I’m reading Ethel (Vertebrate, 2024), Helen Mort’s new biography of Sheffield-based countryside campaigner Ethel Haythornthwaite, who raised money to buy the Longshaw Estate in 1928 and save it from development. A 1930s pamphlet, reproduced in the book, shows Longshaw with the caption “Saved for the Nation”. The second half of the book is Haythornthwaite’s long-form poem The Pride of the Peak, her celebration of place and season, which becomes my guidebook for the afternoon.

Castleton, in the poem, is a “little limestone town aside the hills / … Where white spurs jut and strange enchantment fills / The heart delighting…” The area is peppered with visitable caves and “rare blue veins in arches cavernous”. You can buy jewellery made from Blue John, a mineral unique to this area, in the town’s shops. The bus route ends near Blue John cavern (£19/£13) winding slowly up through “huge hills of green”, chalky turrets and towering silences.

Next morning, I stop off at Haddon Hall (£26/£24, under-15s free) to walk through its airy Tudor gallery and gardens full of irises, peonies and cascading scented roses. Arriving by bus, which is easy, gets you 20% off entry. With flowery gardens clustering around its old grey walls, Haddon Hall is a great contrast with the epic scale of Chatsworth. There’s a smell of meadowsweet as I cross the bridge into the grounds from meadows rich in yellow rattle, ragged robin, clover and cranesbill to a restaurant in an old stable block.

My Derbyshire Wayfarer ticket is valid right across the county on almost any bus except the open-toppers and I decide to spend my last day or two exploring the less-crowded towns and villages of south Derbyshire. Besides the buses, there’s a train from Matlock, which takes half an hour to Derby along the little Derwent Valley Line, crossing and recrossing the winding river (£8.10 day return, eastmidlandsrailway.co.uk). It passes Cromford Mills, where Richard Arkwright created the first water-powered cotton mills in 1771.

But I catch bus 6.1 from Haddon Hall back through the well-connected Derwent valley. This area is packed with classic attractions – cable cars, children’s farms, theme parks, several with rewards for car-free visitors. White Peak distillery in Ambergate offers a free hot drink; there’s discounted entry to the Heights of Abraham in Matlock or Crich Tramway Village; and 10% off in the café at Cromford Mills.

Stopping at hilly Wirksworth for lunch, I visit St Mary’s church and find T’owd Man, a medieval carving of a lead worker with his pick and kibble (basket). In the nearby Heritage Centre (£5, £1 for accompanying children) there are tools and stories from the local lead-mining industry, and some reading glasses that belonged to George Eliot’s aunt. From Wirksworth it’s 50 minutes further to Derby for my last night.

This city, with quiet shopping streets and crumbling infrastructure, does not have a great reputation as a tourist spot. But I always find it a friendly, affordable base for visiting the Derbyshire countryside, with sundry charms of its own. Last summer, I visited the new Museum of Making (free), walked along the river to Darley Park, with its candyfloss-huge summer hydrangeas, and caught a bus to Spondon for a stroll through fields and an ice-cream at the Bluebell Dairy.

This year I take a solar-powered electric boat trip up the Derwent looking for kingfishers (£8/£6) and stroll over the bridge to the Exeter Arms for a perfect garlicky slice of Homity Pie and a pint or two of the Dancing Duck brewery’s moreish pale ale. From the top floor bar of Derby’s riverside Holiday Inn (doubles from £80 room-only ), next to the bus station, there’s a sunset view. I can see distant wooded hills beyond the tall cathedral, where peregrine falcons nested again this summer.

Bus 114 to Kedleston Hall (£18/£9) next morning leaves from nearby, takes 25 minutes and arriving by bus earns me a free cup of tea. The path from the bus stop brings views of the Palladian bridge and long lake. Kedleston has miles of birdsong-filled woods, and the house, designed by Robert Adam, includes a columned marble hall and Blue John vases.

Back in Derby, there’s just an hour or so before my train leaves. I have a drink at Electric Daisy, a flowery new beer garden and event space. Its creator Jamie Quince-Starkey is watering wooden tubs of fruit and flowers as I arrive. He talks about creating urban spaces that strengthen our relationship with nature.

“The Derwent connects Derby with the Peaks,” says Jamie, discussing bold plans to make Derby “the ecotourism focal point of the whole country. The idea doesn’t feel so far-fetched from my perch under a sunny arch of clematis among raised beds of strawberries and rhubarb, fragrant fennel and lemon balm. As I walk back towards the station, there are wagtails hopping by the river again, and a warbler is singing in the trees.

Accommodation was provided by the Ashford Arms and Holiday Inn Derby Riverlights. Travel was provided by East Midlands Railways, Stagecoach and Derbyshire County Council. More information from Visit Peak District & Derbyshire and Visit Derby.

• This article was amended on 28 August 2024. An earlier caption on the first picture said that the Peak District and Chatsworth House were easily reached from Derby on the Peak Sightseer bus. In fact Transpeak runs hourly from Derby, which would connect to the Peak Sightseer in Bakewell.