gdgt

"Busy" means "recharging", and there's really not much you can do to make the onboard flash charge faster. The one approach I've seen anecdotal evidence for is to get a battery grip and install two batteries - this can supposedly supply more current and recharge the flash faster. But given the cost and added bulk of a battery grip, you're probably better off with a dedicated flash unit if fast recycle times are what you're really after.

MtnSloth's suggestion of using a Speedlite is probably the most sensible. The 270EX II should be sufficient if you're only looking to use it in the same way you use the onboard flash, but if you want to get more creative, the 430EX II is significantly more capable and not ridiculously expensive.

The workaround to problems with the built in flash is an external flash. Canon's Speedlite EX series should be your preferred options; but any third-party flash that supports Canon's E-TTL II autoflash should work. User reviews from the bigger online retailers like B&H should be helpful in avoiding mistakes; but I tend to start my research at places like gdgt. However, I think gdgt decided to exclude camera accessories from their database. So you may be better off starting at places like:

www.the­-digital­-picture.com­/Reviews/
www.popphoto.com/ (and their forum > forums.popphoto.com/ )