With 3 weeks available should I buy a motorcycle or be part of a tourist pack?

[MyOwnWay]

Hi everyone, as it is getting colder here in this part of the UK (London), I was thinking about riding in some warmer country like Mexico, for instance.
I was granted 3 weeks off work from the very end of this month till 19.02.2012 and my first thought was towards buying a motorcycle in the USA, not far from Mexico, so I would get the bike sorted and ride down as far as it is time for me to go back or do something with the machine.

Somebody from this site offered to help me with almost everything but in the end he thought he would not have time to deal with the different aspects so...I came back to the beginning of the dilemma : It is worth the pain of looking for a motorcycle, seeing if someone can help to title and register it before I get there? or should I sadly give up the riding idea and buy an organised tour pack in an agency rather than staying at home drinking coffee for 3 weeks trying to warm up a bit?

The problem for me would be trying to get the paperwork done so I don't have to get there and start from zero risking to get stuck and not enjoying my time. Also storing or selling may be a problem unless it is done by the same person who sells at the beginning of the trip and buys back at the end.
Europe must be cold in most places now otherwise I would go for a European tour.

Any thoughts, tips, suggestions??

Thanks.

Marco