I'm not sure what environment you're working in, but because UTM zones are referenced to a unique central meridian, the longitude of a point should be within six degrees of the central meridian of your target UTM zone.
Regarding a projectable/renderable bounding box of a UTM zone, ESRI datasets that come with ArcGIS should contain a UTM zone shapefile, but you could also roll your own pretty easily. The northing coordinates will always be 180/-180, and simply walk your way through every 6th line of longitude, and there are of course 60 zones in the world.
You'd have to watch out for the exceptions Dan mentions in his comment.