If you follow the link in a previous answer you will see that there are several ways to qualify for a contextual offer at Bristol - the most common are that you go to a low-achieving school or that you live in a postcode with a low University progression.
If you qualify, and you get an offer, the Uni will automatically give you a lower offer. You dont need to do anything - their data system spots the relevant applications - and no, you are not more or less likely to get an offer, its about the terms of the offer not the offer decision itself.