Jo, why is your Realtor advising you to bid up? As Dave below indicated he must have a reason for his suggestion and you'll want to know it. There must be some information that he has gained access to that has prompted his advice. Get that answered to your satisfaction. Good luck.

First ask this question of your agent. Your Realtor should be able to give you a reason that makes sense to you. Your Realtor should already have given you a current CMA (Competitive Market Analysis) on the home. I don't know your market (I'm in California) but unless your market is going up substantially, or there is some other justification, I would be hesitant to advise you to bid more than the CMA price indicated unless you are certain this is the one and only home for you AND you are certain you're going to live in it for at least five years.
I can think of several scenarios that could create this situation. Your Realtor may know that several other buyers have viewed the property recently. He or she may know that other offers have been received. They may know (or have recently learned) the price of a bid the bank or seller has rejected.
Start with your Realtor. If you can't get an answer you can understand (even if you don't agree with it) you might want to consider a different Realtor