The sediment is a result of yeast growth that occurs when you feed them with priming sugar. Just decant the beer into a glass, leaving the sediment in the bottle. This is a relatively traditional way to carbonate. If you don't like the sediment, you'll have to keg.
Here's a tip: If you're going camping or to a sporting event (or any other function in which sediment is undesirable) you can chill down another bottle (sanitized) and decant a bottle of beer into the new bottle. Pour slowly, only allowing it to foam at the end. Cap on the foam (to reduce oxygen exposure), and you should lose very little carbonation.