Can you drive a motorized scooter on shoulders/in bike lanes?

I'm considering a cross country trip on a motorized scooter (sort of like a Vespa type thing). I was originally planning to do it on a bicycle, but I realized I don't have the endurance for it. However, I'd still like to follow the route I've read about for bikers (which follows roadways, but is always driving on shoulders or in bike lanes).

Are motor scooters allowed to do the same thing? What is the general rule for this? Is there a speed cap?

Thanks

I wanted to add that I'm not looking to get a big 60 mph scooter, but something I can comfortable average 15-20 mph on (basically, bike speed) is fine.

49cc scooter laws are different in every state. Yours may not require moped registration, insurance, or wearing a helmet . . but you could be cited for not having insurance, or for not wearing a helmet, in another state. Related links . .

(this one may take a while to load)
http://www.horizonsunlimited.com/tstorie...

These 2 morons apparently knew very little about maintaining a scooter.
http://intransit.tv/travelers
Granted they were very cheap China scooters, but if properly maintained (frequent engine and rear gearbox oil changes, periodic valve lash adjustment), the 139QMB 49cc 4-stroke is very reliable. Support resources . .
http://www.partsforscooters.com/Find-Rep...

Related scooter forums . .
http://www.urbanscootin.com/forum/
http://scootdawg.proboards59.com/index.c...

It depends where you do it. In CA it's illegal.

In most states if the scooter is under 50cc it is okay to ride in the bike lane, not on sidewalks. If it is over 50cc it must be ridden in the road and you must have a motorcycle endorsement. It varies by state, but that is pretty much how most of them go about it.