The tunnels are tarmac, and go SE from Bath.
So you could do Bristol to Bath on railway path; up and over the Avon on A3604, R@TL to base of tunnels path [Bellotts Road]; up though tunnels; emerge at Tucking Mill and go down through Monkton Combe.
Not sure where you want to go next? I think last year featured Colerne?? In which case you have the choice of the A36 and dive down through Bathampton, or along the canal towpath [reasonably benign] to Bathampton. Either way you may well stop at the George Inn on the canal, before crossing the toll bridge over the river..
Other options might include - Bradford on Avon, Corsham, Biddestone, Yatton Keynell, etc.
[ETA: The BoA option is the NCN254]