REO Question

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Hi,

I bid on an REO last Wednesday. The REO was listed 27 days ago and currently has renters in the house. The house is immaculate and listed at 199,000. It sold in 2005 for 260,000. My realtor suggested I make an offer of $185,000 and request the bank cover's my closing costs. I am the first and only offer as of today. My question's are ... Should I have bid more? If another offer comes in for more will they accept that offer or let me know what the other offer is so I can offer more? Or any other insights you would have on my situation. I am asking as I was the second offer on another REO and my offer was rejected. I don't want that to happen again.

Thanks!