I think you can assume that if Liverpool offer you a place, it'll also be conditional upon a Foundation year (or going and finding yourself a Maths A level); I don't think that Bath offer an FoE programme, so that's probably why the rejection.
I have a close colleague who until 2 years ago was teaching on that course at Liverpool. So far as I can tell, he only left because they wouldn't promote him, and still speaks very highly of the course - certainly professor Padfield, who runs that department, is extremely well regarded across the UK aerospace industry.
G