I use Bristol quite a bit as a holiday airport and feel that I've got my head around how to avoid being ripped off.
You are right to target your search south of the airport - further down the A38, not on the Bristol city side of the airport.
You don't say whether you have a car with you - but if you do it can make quite a bit of difference to the overall cost.
Bristol Airport Holiday Inn is on the A38 - about 3 miles S of the airport - and it does a 24/7 shuttle bus for a very reasonable £2 per person per journey. But it will charge you for parking your car (rates vary so there's no point in me suggesting rates).
I have logged this place on my last journey.
http://www.themendipgate.co.uk/
It is at Churchill - again on the main A38 a little further down. My taxi driver last time told me about it last time around, but I've never stayed there (so can't specifically recommend it). If you go on that website you will immediately realise they are geared up for catering for folks such as us.
Whatever you do about taxis, DO NOT use the airport taxi operator - Checkers - if you value the contents of your wallet. Because they have the monopoly, they charge high rates.
Hope that helps.