Why do you think you need a template bushing in the first place? Unless you have jigs that were designed to be used with a 5/8" template bushing. I'm not sure what you're gong to use it for...
That said, do not use a 1/2" bit with a 5/8" bushing!
Here's why: a 5/8" template bushing does not have a 5/8" hole in it! The 5/8" measurement represents the outside diameter of the bushing. The hole that goes through the center of the bushing is actually smaller. Probably much smaller. Even if the hole was 5/8", that only leaves 1/16" clearance around the outside of a half-inch bit. Ideally you want more clearance. Probably a lot more, especially if you aren't using a centering cone to ensure that your bits are perfectly centered in the template bushing's hole.