I was under the impression that most SatNavs have some form of internal battery, especially as nowadays they are quite small and designed to be able to be taken with you and assist you on foot if neccessary.
I have an 02 XDA PDAphone that has GPS built in and TomTom installed, and I have used it on my bike a little bit. With my phone I'd guess the battery would last a little over an hour when using the GPS. If there was a mode that would just give you audio instructions while powering down the screen, it'd probably last longer.
There are ways to charge your phone/GPS unit from a bike dynamo, but most of them are DIY and you need to able to solder together a simple circuit. I did find a company in Australia who make a
solar/dynamo powered phone charger, but I don't know how much it costs.
I would suggest panning your route, taking a map, and taking the TomTom for in case you get lost. You won't need the TomTom on all the time then so the battery life won't be a problem.