On bank foreclosed or REO properties, much depends on the Realtor. I have received responses back the same day, but usually within a day or 2. Short sales, are a different story. My buyer & I made an offer on Sunday, the bank countered on Monday, we countered back, bank accepted the same day. The listing agent and the asset manager for the bank were great inputting the info to the bank. My advise is to use an experienced Realtor dealing with REO properties.
Unfortunately, you are dealing with an institution rather than an individual that you could meet and communicate with face to face. The bank will take as long as it wants to, to go through their bureaucratic process. Good Luck.
Adding a response time has little or no effect on the bank's response time frame.
I wish you smooth sailing.