Yes there are busses that run from Yas to Abu Dhabi and although very cheap, the journey will take quite a long time due to all the stops. You may wish to consider a taxi which would cost you arounnd 60-80AED (10-15 GBP) and is much quicker than the bus. Some of the hotels also run a shuttle service.
Check out Abu Dhabi - Suburbs route. almost 6 years ago