There are a few places to stay listed on the Drayton Manor web site, though most are hotels rather than B&B
http://www.draytonmanor.co.uk/ParkGuide/WhereT oStay.aspx
The nearest town is Tamworth, so if you find a B&B there that will be close.
Here is a map showing where it is, see Drayton Park in the centre, with Tamworth just to the north of it.
http://maps.google.co.uk/maps?hl=en&q=tamworth &um=1&ie=UTF-8&sa=N&tab=wl
Sutton Coldfield and Lichfield are also nearby.
Note that Thomas Land, while very well done, is quite small and the rides are small, so it does fill up very quickly.
Try and go on a quiet day if you can, not over Easter weekend for example !.