There is a frequent bus service from Preston Bus Station using routes 19 & 19a (recommended) as well as 23 & 22 (which are the best if you are coming from the train station).
From the No 22 service terminus at the the Royal Preston Hospital. and the No 23 service stop at the entrance to Sherwood Way it is a short walk to the Exhibition. The 19 and 19a stop right next to the college.
For directions for Buses to The Exhibition from Preston Railway Station click here.