Wells is quite well connected by local buses which regularly run between Wells and the towns of Bristol, Bath, Weston-Super-Mare, Shepton Mallet and Glastonbury.
The document link below takes you to a Wells Bus Map on the First Group website. Schedules and routes may change throughout the year so please check their website for any changes that may have been made recently.

Web Site: www.firstgroup.com

Document: www.firstgroup.com/ukbus/bristol_bath/assets/pdfs/journey_planning/maps/somerset/Wells.pdf