Celtic Manor not too far away - might be a bit pricey but winter rates are pretty good as far as I remember and bound to be in top condition - don't be put off coz it's worth checking out i reckon
There is loads of choice around the Bristol area-Bristol and Clifton is one of the best and Long Ashton is superb, The Kendleshire is also one to consider, im not sure of the availability of tee times on weekends but i'm sure you'l be able to get that information from their web sites.
Bristol & Clifton is a good shout Paul, Clevedon is another that is worth a look.
I actually live in Bath, which is within 15 miles of Bristol. There's some excellent courses nearby including Cumberwell Park, Bowood (near Corsham), Kingsdown, Bath Golf Club and the Manor House (Castle Combe - just off the M4).