I know it's not close to Ambleside but worth considering if you're thinking of going to Keswick or over towards Penrith -
Penrith Truckstop has male showers - £2, apparently no facilities for ladies though :mad2:
At quieter times (weekends and mornings) ladies might be able to use the mens with someone standing on guard outside.
Tebay Truckstop (just off J38) has shower facilities too - not sure how much but probably similar priced. Not sure if there are ladies showers, will check next time I'm there.
Edit : have just checked with J38 Truckstop and there are both male and female showers £2.50 each or free with overnight parking. There is free wifi in the cafe which does an all day breakfast for £4.99.
Most Truckstops will provide showers although sometimes you have to pay for overnight parking to access them but for a one off, overnight at a Truckstop is worth considering as it's normally under a tenner, is safe and secure, there's plenty of space (especially at weekends), there's usually a shop and cafe serving a good slap up cheap breakfast, decent loos etc. Make sure you park away from refridgerated containers if you want a good night's sleep.