We're using analytics API to get number of visitors and would like to filter the visitors who are backing right back. Is there a filter for that?</div
I have looked a while into the docs and I don't think there is a filter specifically for bounces (i.e. a filter that uses the same definition for bounce as the reports). However it should be possible to find a close approximation.
One approach is to filter for users for whom page depth equals one. This not necessarily 100% correct, depending on if you want to count users with one page but with interaction events as bounces or not. You might want to combine page depth with "session duration equals 0" (as GA cannot compute a session duration for visitors with just one interaction). That will give you for users who bounce (your title and your questions seem to ask for the exact opposite things), if you want visits without bounces do page depth > 1 and session duration > 0.</div