By A string bar chords, I presume you mean A form like C at the 3rd, D at the 5th and so on. You aren't barring the 6th string, right? You don't need to play that one.

You can largely get by without using the full bar if you don't need it. Don't worry about not getting a clean high e if you can't get it right off. Just target the first 4 strings of the bar. That will make the chord easier, and you will get it full on eventually.