You'll probably get mixed reviewed on using bottled water. A lot of water conditioners have additives specifically for your fish (like the Tetra I use has compounds that are supposed to help keep his slime coat intact and healthy). Bottled water is definitely better than distilled, which is sterile, lacks minerals, and is generally baaaaad for your fish.
I think your method of changing the water sounds fine. :) As long as you get the old water out and new in, right? To be honest, I just use my hands to corral my betta. And he knows he's getting a bloodworm once he's in his cup. lol Some bettas are more prone to jumping than others. I think whatever you're comfortable with when it comes to changing his water is fine as long as it's effective. :)