I'm assuming that you're using whole hops and not pelletized form. In this case, the leaves will remain floating pretty much indefinitely. As such, when you're done dry-hopping, you'll want to rack to another vessel. Use a homemae racking filter, or a racking cane tip when you do so. Since the hops float, when you do rack, you won't have to worry about the hops clogging the racking cane until the very end. When you do get to the bottom, some hops leaves will undoubtedly clog your racking operation, thus slowing down the flow. Just keep going until you no longer have any flow, and then you're done. You'll certainly lose some amount of beer, but such is the life of a dryhopper.
I recommend not going directly to bottling from there. Let it settle for another week. Of course, a small amount of hop leaves will make it through the racking cane and into this tertiary vessel...but, when you rack from there into your bottling bucket the following week, chances are very slim that any of these stray leaves will make it into your bottling bucket. If they do, they'll probably float, so you can pick them out of the bucket with a sanitized handheld strainer.
