Advice Needed : Trying to make my first offer

I have a buyer interested in a downtown condo. I did find a REO which I think they might be interested in. Now here's the problem:

If I make a offer, and the offer gets accepted, but the buyer isnt interested, and wants to keep looking. ...I dont think I can find an other buyer for this property because this is high priced, exotic condo and I dont know anyone else who is looking for similar units.

So, I dont know where to start. Make offer, if accepted, show buyer, if No... proceed to make offer on other one & so on???

""Or is there a way I can get the buyer's acceptance Between my offer accepted and prior to me signing the contract with seller ?? " Of course, in a safe way....so the buyer wont bypass me and deal directly with seller.