We used to have this problem when we were shrink fitting carbide inserts into hardened steel die cases and steel inserts into steel die cases. It was really evident on pieces requiring an excessive shrink fit (customer mandated). If the surface contact area isn't too long, the method I used is as follows:
1) Get a table oven preheated. In your case, I'd guess around 400 (make it well below your tempering temperature).
2) Put your shaft in a freezer in the lunchroom.
3) Put your bushing in the table oven and let it heat thoroughly, maybe 30 minutes or so.
4) Now comes the tricky part. Not knowing the length of your part, I'd say you'll need two propane torches. The tips should yield a dispersed flame rather than a concentrated one. Watch your oxygen content also as you can really soot up a part if it's too high. Preheat a plate or flat surface with the torches. Not red hot but hot to touch.
5) Make sure your freezer with the part is nearby. You'll likely need two people for this process until you get the hang of it. Then get a telescoping gage and set it for roughly .002"-.003" greater than your shaft diameter.
6) Pull the bushing out of the oven and start to heat the outer and inner surfaces with the torch. You want to keep the flames constantly moving over the entire surface. Have your 2nd guy there to check the ID with the telescope gage and make sure the shaft is handy.
7) Now the tricky part. Once you've torched the bushing to get the ID expanded enough, insert the shaft. If your parts aren't the same length, you're going to have to come up with a method for holding them in position. If they are the same length, a heavier flat plate or scrap piece of steel works well.
8) Immediately after inserting and positioning that shaft, you want to spray the outer surfaces of the bushing with a cold air gun. Regular shop air will work, but the cold air gun is better as it will give you a faster quench. Your parts should be solid after about 30 seconds. After they're set, keep hitting the surfaces with cold air until they're cool to touch.
If you had your flame right and you got your parts cooled quickly enough, you should notice no degradation in your macro-hardness. Essentially, you heated the part but didn't give it enough time to transform the microstructures significantly.
When you get good enough at wielding two torches and fast quenching, you can often cut out the preheat step. It depends on your part sizes. Note that your outer surfaces WILL be discolored, but that's common.
