As Jeannine says, activity really varies from area to area. It also depends on how good a value your property is.
It sounds like you've had real good activity.
However, recognize that most of the activity is likely to occur during the first couple of weeks of a listing. It's great that you already received an offer. You don't provide enough details to suggest whether the offer was good, other than it wasn't what you wanted. Sometimes people look back in regret at that first offer they turned down. And that raises a question: How motivated are you? You say "VERY" and you should be if you have a contingent offer on another house. In that case, your first priority should be to sell your present home for an amount you can live with, not "want to get the most $ for our current house."
What did your Realtor say?
And, umm, an offer on another home in THIS market contingent on the sale of your present home? Bluntly speaking, that wasn't the best idea in the world. (I know, I know. You fell in love with the new home. You just had to have it. Still, not a good idea.)
If you think you're motivated now, consider how you'll feel with about 7 days left on the contingency on the new home.
It's fine to sell your present home for a reasonable price. And if there's a certain bottom line that you absolutely need in order to be able to buy the new home, then, yes, you have to stick with it. But the statement that you "want to get the most $ for our current house" doesn't sound right in the situation you're in.
So, to answer your question, your activity probably is quite good. Determine the need for a price reduction (when and how much) based on the level of activity for the next few weeks.