You're going to be attempting a fine line of enough yeast to consume sugars to properly carbonate the beer versus reducing sediment in the bottle.
The sediment you're seeing could be a variety of things generally there are a few best practices.
Limit trub and other particulate from the boil that makes it into the fermenter.
Limit particulate from fermentation that makes it into the bottle. This can be done by the following:
- After primary fermentation is complete (a gravity reading stable over the course of several days) reduce the temperature of the fermenter to near 32°F (0°C). This is called "Cold Crashing". This will encourage yeast and some proteins to fall.
- Transfer to a secondary storage vessel. This IS NOT secondary fermentation as many people will call it, but you're not adding anything fermentable.
- You could add some type of fining agent (I prefer gelatin-finings). This should be done with caution as removing too much yeast could impact the necessary bottle fermentation for carbonation.
- Hold storage vessel at near 32°F (0°C) for a week or so.
- Rack to a bottling vessel leaving anything that has settled out behind. (I would suggest adding an extra 1/2 gallon (2 litres) (assuming a 5 gallon batch) to your batch size to allow for buffer.)
The problem you may run into is as mentioned in the fining item. Removing too much yeast before bottling could impact carbonation. The best case is you'll reduce sediment but it will take longer. The worst case is you'll reduce it to the point that too little yeast is present and they will over work to consume the sugar. Over worked yeast = high potential for off flavors.
All that being said the BEST (in my option) method for a home brewer is to stop bottle carbonating. Kegging then bottling off the keg when bottles are needed is what I do. I say this because I am not a fan of most filtering systems out there. I don't think the risk is worth it when doing the above steps (minus bottling) will produce very similar results.