In reply to johnboybuchan:
Not much worthwhile that's a short ride from Barrow. If you don't mind getting in your car (or doing a fair bit if tarmac bashing on your bike) then you have one of the best areas in the country for mountain biking nearby. Plenty of ride guides on the internet
Edit: if you've just moved to the area then I'm guessing there's a reasonable chance its for a job either at the yard or the hospital. If the former there are a few informal groups that head out in the evenings. Both shops in Ulverston (Velo Cycle and Ride Bikes) also do group rides
Post edited at 22:39