Hey, you should 100% apply, those are A2 requirements of AAB, with your ABB you could easily get that up to AAB for A2; I can almost guarantee people will get offers with grades of around ABC, ACC (probably no lower than this though). Also remember that universities take a holistic look at your application, and your personal statement will play a large role in whether you get an offer or not (your GCSE will probably also be taken into account).
A2 predicted grades, at least at my school are decided by your teachers and if you can convince them that you will work hard enough to get the predictions they'll almost certainly give you your desired predicted grades; it does help if your teachers like you though :P
Btw, congratulations on your great grades. Also, my AS predictions were quite far off what I actually got