There is also Blacks (a few doors down from Oswald Bailey), Millets (Broadmead) and Taunton Leisure in Bedminster.
You don't need to get everything the first time... you continually add to what you have to make your life easier/nicer etc. And there will be stuff you realise you have forgotton - for us it was anything to cook in the first time but the site had a shop where we could buy from and a trip to Tescos got a washing up basin.
If you can get to Highbridge it's worth a trip to Highbridge camping, they have a big display of tents. Also Taunton Leisure have a display at the Garden Centre in Highbridge (can't remember its name sorry).
There is also Kingswood caravans who sell "stuff", I'm not sure that they have tents. I've also seen reference to the garden centre at Bitton having tents but have not been there.
As Summerdsys says, you can get away with taking bedding/pots/pans etc. from home first time out to see if camping is for you.
edited to say that Halfords have tents, you will prob need to do web research first as they don't usually have any tents up.
Does the A38 down here get the record for the most camping displays on it? From Bristol down you get to do the Garden Centre at Highbridge,then Highbridge Camping and if you keep going you get to Somerset Camping at Taunton. I hadn't realised that Attwools was on the A38 in the other direction!
Got our tent from Jarrets garden center,gbcamping there called.They had a number of tents on display and also had a sale on when i last went there 3 weeks ago to buy our tent,cheers Gaz
Amazing family weekend with old steam engines, classic car displays, market stalls, and full catering and bar. And camping on site - Save £25 by booking in advance.