Why does my front tire wobble? - 2004 Honda VTX 1300

This could be your wheel bearing,raise front end on bad tire side and grab tire and move it around to see if it is loose,http://www.autozone.com/autozone/repairinfo/repairguide/repairGuideContent.jsp?fromSearchPage=true&pageId=0900c15280265793&partName=Front+Wheel+Bearings&partId=0900c15280265793

Have you checked the tires ?
Sometimes a wobble can be a broken belt inside the tire tread.
Or it could be something loose in the hub.
You could also switch the front and rear tire to see if the wobble moves.

It wobbles? like when your driving it vibrates and stuff. If so its not your tire. It could be anything. Loose lug nuts. Bad Hub assembly. Suspension. Brakes. or if it really is the tire. it might be out of round. or need to be rotated to the back of the vehicle

problems like this are best discussed with an accredited bike shop who has experience with wheel wobbles
you have changed the front tire to radial but did you change the back tire at the same time as radials and cross ply ( bias ply) tires have different handling characteristics
the wobble may be like a lack of compatibility between case constructions and I am thinking this because you say that the problem goes when changing back to the bias ply

you need to have your tires checked for a slipped belt, also if you get a shake in the steering wheel when you apply the brake you need to have the brake rotors re-surfaced or replaced.

Did you line up the dot on tire with the valve stem ? if not break tire down and line up bal dot and re bal. If it is taking alot of weight try relocating tire on wheel until you find a better bal position that dont require alot of weight.
I have had new tires cause wobble , spin tire on bike and check for wobble in new tire.

Wheel needs balanced anytime you replace tire. Wheel could also be bent, but not as likely.

i'm not an expert but i had a simular problem with my honda and though lots of questioning mechanics i learned that the front forks must be balanced in oil and pressure

Check the passenger side tire.

yes make sure your lug nuts are all tight and the wheels are seated properly on the hubs, if they are tight bring the car to a tire shop and have them balance the two front tires, this will tell you if you have a bent wheel please rate -jeff