I'm remembering an analogy from school here...
Electricity is a lot like water in many respects.. voltage can be likened to pressure and current can be likened to a volume of flow... Strangely, a battery can be looked at like a water tank..!
Ok, Imagine the cold water tank in your loft... The supply gives a constant maximum fill, but the flow is determined by the water level in the tank ... the ball-cock shuts off supply as the level in the tank reaches a maximum.
Ok - now start turning taps on in the house ... the basin taps, pah - not much water flow there and the ball-cock opens slightly, overall tank level maintained... Kitchen taps too... ball-cock opens more, more water flows into the tank, level maintained. Bath taps now ... hmmm ball-cock is fully open and as much water flows from the tank as flows into it so the overall level is maintained. Now... switch on the garden sprinkler - the ball-cock is already flowing as much water as it can, but there is more water flowing out of the tank than is going in ... If this combination of demand continues, then ultimately, and despite the ball-cock being fully open, the tank will eventually become empty.
The battery on the bike is a 'tank' and can hold a given amount of electricity (the amp-hour rating shows this..) The alternator is the supply, the regulator/rectifier is the equivalent of the ball-cock and the devices we run from the bike are the equivalent of the taps inside our house...
The alternator gives a fixed maximum output, the battery can store a certain amount of electricity, but if the demand we put on the system exceeds the storage capacity of the battery it will eventually go flat. End of.
There's been a recent thread on almost exactly the same subject - you just need to be aware of the limitations of the alternator and make sure you've got sufficient charging current left to ensure a healthy battery. A 'bigger' battery (one with a higher A/h rating - but would it physically fit?) won't solve the problem, but being aware of how much juice you're using will..
Greg