One thing you can do on a big hole is coat the inside of the hole with superglue, let it dry fully, and test fit the bushing again.
Let me say this again - LET IT DRY FULLY. If you can "smell" the superglue, its not dry yet. Superglue takes in humidity (water vapor) from the atmosphere to dry. In cooler (dryer) weather, this is going to take longer. Just let it sit a day, to be safe.
If the bushings are still too loose... recoat the inside of the hole. The superglue will stiffen the fibre and add thickness... some rigidity to the edges of the hole... Its not a bad fix really.
The bushings should be a medium press fit. I'll sand the holes on guitar necks. I just dont like a force fit on the bushing in the wood. No "driving them in". I like to get the ones on guitar tuners to the point that they can pressed in pretty easily with a screw vice. A screw vice is simple a 1/4x20 screw, a flat washer on the bushing, a rubber washer and another flat washer on the back of the headstock, and finally a nut. Using that.. nutdrivers alone will be enough force if the fit is "just right". Wood can swell, wood can shrink. Having a REALLY tight tuner bushing..... its not outside norm of thinking to consider a split headstock.
On a bass tuner... same thing, but a larger screw for the makeshift vice.
In your case.... just build em up a little. Use a Q-Tip with glue on it. If ya get some cotton on the inside of the hole... leave it, its filler!~