이따 봬요 is right..
Hum... they are quite confusing :P
봬요 is shortened from 뵈어요.
You can say 뵐게요,뵙겠습니다 meaning the same as 봬요, not 봴게요,봽겠습니다
However you'll say 어제 선생님을 뵀다(past), not 뵜다.
There is a way to distinguish which is right
If you put 해/하 instead of 봬/뵈 in a sentence then, if not awkward, you'll use it
해-봬 // 하-뵈
내일 봬요>> 해요> 해요 sounds right
내일 봴게요>>핼게요> dosen't make sense but 뵐게요>>할게요 does right,, so you'll say 뵐게요.
You can also use this way to 되/돼>>>> 의사가 되다>>하다, not 돼다. 숙제 해야 돼>>해, not 되
It's quite confusing one even to most Koreans