Public transport in the British countryside is generally considered to be pretty weak, even by other people in the UK. What transportation does exist, tends to run irregularly and erratically, and will often shut down very early in the evening, and may not run at all at weekends and on public holidays. This can make getting out and seeing attractions around your B&B very difficult if you won’t have access to a car during your stay. If you’re feeling confident, then it’s worth asking if you can hire a bike and take advantage of the National Cycle Network and other paths and trails around the countryside.
If you do want to go out, then be aware that cabs can also be relatively thin on the ground, although the B&B owner will probably be able to recommend one. If you do decide to go for a cab, then be sure to book the return journey well in advance, (if possible, before you go out), to avoid the risk of being stranded far from your accommodation late at night. That can often be a costly problem to fix.