I made a tele bass for my girlfriend's daughter last year. I used a standard telecaster body pickups and all. I modded the stock bridge, and added a mustang bridge at the correct scale length. I used a 30" scale bass neck. I was surprised at how good it sounded and played.
It would be tough to use a full scale neck. It's going to be neck heavy, and the bridge would be really close to the edge of the body. The neck pocket won't accept a bass neck so you will have to route it to fit. It's not impossible, but it can be done. I'd surf ebay for a bass body instead. You should be able to find plenty there.
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^^^ That's incredibly hawt. I wish Fender would make a production model exactly like it with a short scale blocked neck just like yours and a tele style headstock. I'd use a Dano lipstick pup at the neck and a Fralin vintage single coil or Dark star pup at the bridge.
Also to the OP - do you know about warmoth.com?