So I'm a little worried about getting flamed, but I'll say this anyway:
IMHO, wickedmax, your set up isn't too bad, provided you keep up with the water changes. But, of course, having said that, I'd also like to emphasize that it could be much,
much better. Please do consider getting a bigger tank for your new little friend, one with a good filter and lots plants to break up the current-- he'd appreciate it, I'm sure.
I do have a suggestion for you, though, if you decide to tough out your current situation. I've actually seen little undergravel filtration kits made especially for one gallon goldfish bowl set ups. They don't cost much, and would certainly be better than nothing. If the vase or whatever it is that you're using now doesn't have room for the filter, buy a new bowl and move everything over. Hiding the filter intake thingie from view with the bamboo shoots shouldn't be difficult, either, so you can still have a visually pleasing set up.
Just out of curiousity, what are you feeding the lil' betta dude? I know that some vase things are sold under the belief that the betta will nibble on whatever plant is in there with it-- rest assured that the betta living this way is an unhealthy betta, indeed.