You would either remove material from the floor to make it flat, or remove material from the shoe to make it conform. You can't bend oak shoe to very small curves unless you steam it.
If I am refinishing a floor, I have used a hand plane to dress down high spots along the baseboard, then the sanding takes care of the transition to the rest of the floor.
Casey

Thank you for the reply. I had not thought of using a hand plane. I have a small one. I think I'm going to try and use three peices of shoe, and plane down the shoe section where is curves. Thank you! I'm glad shoe is cheap.

Without a picture, I'm just guessing, but I'd say that 3 sections of one foot each won't look normal. (Or maybe I'm just misunderstanding your description.)

As Casey says, remove material somewhere. If it's off the back of the shoe, then the shoe will bend much more. (A sander with coarse paper would also be good for this task.)

You're saying that the curve you need to make is higher in the middle than at the ends (rainbow). I had the same problem a number of years ago. In my case a short section of wall was slightly bowed but the process is the same.

Make a series of parallel (kerf) cuts along the back of the shoe with a saw. Start with 1/4" or so spacing and add more cuts as needed. Obviously you don't want to cut through the visible surface of the shoe. The cuts will make the wood more flexible and give it a place to "go" when you start bending.

Look at figure 4-2 in the link provided. It's not base shoe but I think you'll get the idea

Here is a link that might be useful: Kerf cuts

How high is the bow?

You may be able to just nail one end down and force the shoe mold to follow the floor.