The car hire has a shuttle and is a lot less faff than anything in Bristol, so as a bit of a captive audience I guess it can be a bit more expensive. There is a bus to Bristol or Bath or coaches to Exeter, Plymouth. To be fair for a place not on the rail system it’s connectivity isn’t horrendous and there’s going to be a shedload of roadworks trying to improve the A roads over the next few years.
If you are choosing narrow lanes instead of the A roads, that’s not the airport’s fault. Burrington Combe is nice in daylight. Your main issue is Yeovil is in the middle of nowhere and has shit connectivity north and south. The problem is Somerset (tongue in cheek, winky smiley etc)
I say this as I work in Bridgwater, commuted from south Bristol for about a year (the A38 is perfectly fine as long as you pay attention to read the speed limits), my boss commutes from the independent people’s republic of Yeovil to Bridgwater and Blandford Forum and both journeys are crap.
You could try the Chew road to the A37 but that’s got a few tight spots as well.