Is Bristol bias against private schools??

Yeah I have heard the same. Having said that, a number of people from my school got accepted this year, so don't be completely disheartened. If you really want to go there, then I'd say it's a risk worth taking - also I suppose it depends how risky the rest of your options are. So far 3 of the universities I want to apply for are super dodgy. Yay.

Well the thing is I only got 4A*s 5As and 2Bs at GCSE. And my AS levels could range between 2As 2Bs to 4As. So my grades arent really good enough fo me to feel confident about any of my good choices (Oxford, Warwick/Bristol, Exeter). Im applying for both PPE and Eco+Pol at Warwick. So this is why I dont want to be complacent and put Bristol on my tough selections if my chances of getting in are minimal

Stop looking for praise Your GCSE grades are more than good enough. Oxford probably won't look at them, Bristol and Exeter will give them slight consideration. Even if you only get AABB at AS level that wouldn't be a major disadvantage in applying (certainly not to Exeter and Bristol). Your teachers will probably recognise that you're on the A/B borderline (should you get a couple of Bs) and predict As. Also predicted grades are based on more than just AS level results. What's more there are other vitally important aspects of your application, your personal statement being one.

fair enough, but my teachers are really agitating me about it!

Tell them where to get off. Just make sure you have at least one "back up" option. I won't say safe as there are no certainties in university applications.

Im applying for both PPE and Eco+Pol at Warwick. So this is why I dont want to be complacent and put Bristol on my tough selections if my chances of getting in are minimal

If you do that you will, I repeat, WILL, be rejected.

I (along with several others in my school) applied to PPE at Oxford. Two of those people put Bristol Eco/Pol down on their UCAS, and were subsquently rejected very quickly.
Not because they go to a private school, which annoyingly they went around saying, but because (I think) it would have been perfectly clear from their personal statements that not only were they applying to PPE elsewhere, but also that this 'elsewhere' was probably Oxford. This would have been made clear by the amount of philosophy shizzle written in their PSs, and as such made it clear that Bristol wasn't 1st choice.
One of the Bristol rejectees was later successful with Oxford, and the other was an extremely good candidate who got into a very similar course at LSE, so I doubt Bristol rejected them on academic grounds - however Bristol was well within its right to reject them on the grounds ( I believe) that they weren't a high enough priority with those two applicants. Being in exactly the same position and having the benefit of others previous experience, I suggest you don't do the same.

It really annoyed me when they blamed their rejection on going to a private school. In the grand scheme of life (and uni applications) there is no point at which being privately-educated is a genuine drawback, and I find that suggestion incredibly patronising to state school educated people, who have to struggle for the things we private schoolies get handed to us on a plate.

Well the thing is I only got 4A*s 5As and 2Bs at GCSE.