You can still drink the beer from the bottle, I've known a lot of homebrewers that do this! Personally, I don't like to drink the yeast sediment in the bottom because of "teh gasssss"!
If you are attached the the bottle . . .

. . . you could keg and then bottle as mentioned above. There are also filtration systems that help you get the yeast out, but these (I believe) also require a kegging setup.
What is so great about drinking from bottles? IMHO, you lost the aesthetic pleasure of seeing your beer, enjoying its color and its aroma. Seeing a beer go into a glass, to me, is performance art at its finest.
Just my $.02