I went to Bath for mech eng. With those grades, I would've thought you are a very strong candidate for receiving an offer - you've received the entry requirements and I don't think your GCSE grades are an issue (unless the 6 is in maths or physics). 100% of my peers and those of the year below received a minimum of A*AA at A level.
That said, I don't agree that they ignore personal statements, the staff responsible for admissions say this is a key part of the application.