I suppose that best way to find out if the offer has been presented is just to ask your agent.....! :-)
But just to give an overview...
From my experience, in current real estate market, there are 2 main ways in which a prospective homebuyer would have to deal with the bank accepting/approving an offer on a property. Foreclosures and short sales. In a foreclosure, the bank is the seller. In a short sale, the owners are the sellers, and the bank needs to approve the offer.
The challenge for you and your agent is that banks can be difficult to deal with.
During foreclosures, the listing agent will likely have a well established relationship with the bank who has foreclosed on the property, and the process should flow smoothly, albeit slower than dealing with your typical homeowner.
On the same token, short sales can become an extended process over a few months. The reason for that is... the bank takes forever!!! In this situation, the agent establishes the market value of the property and pushes for bank approval. Some banks are more organized than others, but the listing agent could end up sitting by the phone and fax machine for hours and hours trying to get through to the right people who can make your deal go through.
If you really love the property and you're getting it for a good price, just relax and wait. Ask your buyer's agent how the process is going, they should be able to give you an idea of where you're at. Often times, short sales are approved, they just take awhile.
I hope that helps! Let me know if I can be of further assistance.