It all depends on the bank. Once they have an offer they will approve, they will issue an approval letter. It sounds like the agent is taking guesses. If they had a counter they would just counter. They're miserable for customer service but I have yet to see one counter with a price and when getting it, ask for yet another higher price, unless something was left unaccounted for in the hud and now it needs to be covered.
Put your final offer in writing, have seller sign and submit.

Hi June,
Sorry to say most banks when negotiating prices do it verbally ( that doesn't make it right, it's just the way it's done ) What I would have my agent do is if the bank verbally gives you a counter offer and it is acceptable to you THEN put it in writing, or have the bank put it in writing to sign by both parties. This is how it is usually done.
I'm sorry to hear that you are being "jacked around", but that happens sometimes when dealing with banks.
I hope it resolves for you,
Allyson
408-705-6578
allyson@homesbyallyson.com
DRE# 01397256