Please clarify. What it sounds to me is that the homeowners accepted your offer but the bank who owns their loan needs to approve it. My best suggestion is be patient. It may take weeks or months to get an answer. Depends on the bank and the complexities involved in their mortgage. Don't lock in your mortgage, Don't order an appraisal, Don't line up the moving truck just yet. Ultimately,it's the banks decision as to whether they like the offer and will accept it, so you have to just play by their rules and play the waiting game. I'm not trying to sound negative, but I always say plan for the worst and hope for the best!
I assume YOU are awaiting for bank approval. In the meantime, if you you are going to do repairs, it may be a good time to get estimates if the selling bank will let you in the home. I would push your bank or mortgage company to move forward as fast as possible. I would also get some quotes on your homeowners insurance policy in the meantime.