Hi!
Bantry is a great place to visit but if your not driving you will have limited bus services. Check www.buseireann.ie (the national bus services) and West Cork Rural Transport (they do shorter local services but some routes run only once or twice a week).
Bus eireann have a bus from cork to glengarriff and castletownbere which passes thru bantry. Its impossible to visit mizen head by bus because you need two or three buses and even then you end up in goleen. (check map!)
If you don't want a hotel there is a guest house in town or b and b on glengarriff rd. or Newtown which is a 5 - 10 min walk to town centre. Around 35 -40 eur pp per nite.
Main places to visit near Bantry are
1. Mizen Head and the peninsula inc. schull etc.....
2. Sheeps Head peninsula.. walking ... or driving... buses run 3 days a week...
3. Beara peninsula... inc. Glengarriff... Healy pass...Allihies...
4. I recommend Glengarriff, about 20 mins by bus on same route as Cork (but opposite direction) with Garnish Island... lots nice little shops... Not very central b and b i can think of... good hostels tho...
In Bantry itself... Bantry House is probably most popular...
Tourist offices in bantry and glengarriff and info available in castletownbere...
These are open seasonally.
I hope this helps a bit!!!