There is a trainline to Kendal, from Oxenholme, which is on the mainline from London, Manchester etc. In the other direction, it stops at Staveley and Windermere if you are staying further into the Lakes.

There are also buses running between villages and towns.

Lots of info on public transport here: https://www.visitlakedistrict.com/explore/travel/getting-around-cumbria

You can usually find a taxi at a train station, if you want to book taxis in advance.
Try : https://www.lakesidetaxis.co.uk/

and https://www.bluestartaxis.net/

All terrain mobility scooter hire is available here: https://www.lakedistrictmobility.org/

Bike hire places:

Windermere: https://www.countrylaneslakedistrict.co.uk/

Wray Castle: https://www.brockhole.co.uk/activities/bike-hire/

Hiking & Biking nearby

If you’re staying a couple of days there are some lovely walks and bike rides nearby.

WalkLakes website has maps/routes for different abilities. The National Park Miles Without Stiles lists walks suitable for limited mobility walkers

The Kentmere Horseshoe: Starts in Kentmere village. The Kentmere Horseshoe, is a beaut 12 mile walk, taking in 8 Wainwrights. It’s sometimes called the Kentmere Round, and is one of the longest and most remote walks in the Lake District.

For shorter walks try Hugil Fell and Reston Scar. Only 3 miles with excellent views. www.walklakes.co.uk/walk_226.html

Windermere – Orrest Head. Only 15-20 minutes walk but a great view.

Ambleside to Loughrigg or park in Rydal and do a low level loop around Rydal Water to Grasmere and back.

For bigger walking adventures try the Fairfield Horseshoe. Approx. 6 hour walk starting in Ambleside with fantastic views www.walklakes.co.uk/walk_42.html

Langdale and Harrison Stickle is one of the highest of the Langdale Pikes www.wainwrightroutes.co.uk/harrisonstickle_r1.html

Coniston Old Man ww.walklakes.co.uk/walk_2.html is approx. a 4-5 hour walk.

For Scafell Pike, the highest mountain in England, head up from Wasdale. www.walklakes.co.uk/walk_158.html

ViewRanger is a free mobile app for following off-road walks. You can download OS map overlays for a small cost.

Biking

Three Rivers mountain bike route in Staveley

Biking in Grizedale Forest, about 30 minutes drive or bus ride away