Upton Cheyney is probably the best bet, there are a few ways to get up there. Either directly through Bitton or, turn left at the first roundabout after the Bitton railway station (by Bitton FC) and follow the road through Oldland Common and then turn right just before a vets on the corner (past the ranks of shops).
I do Oldland – Upton Cheyney, Lansdown Lane onto the Costwold Way, across the golf course (on the bridleway!) then down into North Stoke and along the ridge and drop down into Weston village.
A good ride either on cx or mtb. Doubles my journey time but try to do it as much as possible during the summer.
What time do you normally leave (or have to get into Bath)? If you have not ridden it before I could show you one morning.
Edit: Thinking about it.. you can get off of the cycle path just by the vets in Oldland common. That would virtually cut out any main roads (until you got to Bath).