You said it definitely has water. Did you remove the radiator cap to verify that or just look at the plastic overflow bottle? If in doubt, when cold, remove the radiator cap and make sure that the system is truly full.
Then, is the electric cooling fan coming on. If not, often it's just the fuse or switch. Check the fuse first. If OK, find the switch. It should be located in one of the radiator end tanks. Most likely there's one wire to it. If so, that's a ground switch and disconnecting the wire, inserting a metal probe that will reach the contact, then touching to any metal that will allow it to ground, should bring the fan on. If by slight chance the switch had two wires to it, disconnecting the plug and putting a jumper wire in it should bring it on. If the fan comes on then the switch is bad. Replace it. Note: Make sure you have the key on when testing. Some circuits will run the fan even with the key off, but most are wired through the key. I'm not sure on yours.
If not, further trace out the wiring to the fan, checking for troubles. If still nothing, the fan motor could be bad. Hotwiring it from the battery should bring it on. By now, if it's still not working, you should know the whole fan system pretty well and sort it out yourself with logical thinking.
Always the possibility that a thermostat is bad but from my experience that's highly unlikely.
Still another possibility would be that you're being a little too afraid of seeing the gauge go up a little bit. This would be the easiest as it would mean nothing's wrong.
Without knowing what the typical gauge range is on your specific bike, I can tell you that it's not uncommon for them to get up there a bit when in traffic, although never in the red. The fan should be kicking on by about 3/4 of the way up the normal span.
If you're still not sure, have someone look at it who knows. No sense hurting it by overheating when the problem is likely an easy fix. Hope that helps.