Yes, find the 'bike rescue'. it's more or less under lendal bridge, a charity/business to renew shoppers' bikes etc. they charge just £1 per day and you can use the shower facilities too.
It's next to the 'aviva' call centre and very close to train station. The river ouse is literally at the back of it.http://www.bikerescueproject.org.uk/hub-station/
Have a sniff round as well, sum bikes for sale etc...
Ride yorkshire and the north east
Visit the regional calendar here for details---> Update coming soon for 2015