It sounds like you have current drain occurring, probably via the mechanical regulator (if fitted with one)...Very simple to Test....Just remove one wire Ideally the POSITIVE from the battery and insert an ammeter (multimeter set to high amps) Insert the test leads in series with battery....by that I mean connect one test wire to the removed wire and the other test lead to the battery terminal you have chosen.
With everything switched off you should see no current drain at all. You may wish to adjust the multi-meter sensitivity at this time to see if the there is any very low level drain...once again this should be virtually zero. If you do see a current flowing come back and tell us...it's not worth going on any more at this point.
A 5AH battery is easily sufficient, even a 1AH battery will start the bike and then the alternator will keep things charged.
Don't waste you money before testing you might not even need a new battery.
BY THE WAY....IF YOU ARE SAYING THE BIKE DIES AFTER YOU HAVE STARTED? then I would imagine you have a charging fault...Please be more informative with your question to aid speedy diagnosis...
Les