I recently took a Nikon scope of my gun and bought a bushnell. Will the rings i have on still fit the new bushnell? the rings are Leupold Dual Dovetail Medium rings (.770). The new scope is a Bushnell Elite 3200 4-12x40

They should work, both scopes are 1" tube, and are the both 40mm?

Yes both are 40mm

If you had good clearance on your Nikonthe Bushnell should be fine. I know different brand scopes have slight differences in the size of the bell of the scope. Should be fine.

One inch tubes are 1" tubes. The ring height can be the difference. Usually, medium rings are plenty enough for 40 mm scopes.