You can never totally eliminate sediment in bottle conditioned homebrew OR COMMERCIAL beers. There is ALWAYS some sedimentation produced when the yeast eats the sugar to carb your beer.
But I have very little sediment in my bottles. Just usually a little swipe across the bottom of the bottle.
I do it by using a MINIMUM of 1 MONTH in primary (not THREE WEEKS) or more, this lets the the yeast cake compress, giving you more of your beer back and letting yeast clean up and settle. Then I cold crash (but before I was able to do that my beer still had very little sediment form long primary.)
Even beers I secondary I still start with a month. 2 weeks in primary, the a MINIMUM 2 weeks in secondary...but if I'm secondarying it's usually bulk aging and the beer will be in longer and therefore have more of a chance for stuff to settle.
I think a MONTH is a minimum for beers to be given time to clear, in whatever vessel you choose.
Carefully rack to minimize transfer of trub when bottling. Start with your siphon above the trub layer, and don't lower it til most of the beer is racked over (clamp it if you need to) then "Vacuum" the beer off the surface of the trub layer, leaving the trub behind.
Then after the beer is fully carbed an conditioned, letting it chill for as long as possible....AT LEAST a week....again it allows any yeast to flocculate and then lets what yeast does form to solidify and compress in the bottle. I once found a beer in the back of my fridge that was in there 3 months, and you could upend the bottle and still the yeast would not come out. The beer was perfectly clear and even chill haze was eliminate.
Had to blast it with hot water to even clean it, the cake was so compacted and tight.
Even kegging you see this, after several weeks in the keg (I live alone and it takes months to kick 3 kegs) the beer becomes extremely extrememly crystal clear.
I have found over my years of brewing that the key to little sediment, and clear beer really is PATIENCE.
Get a pipeline going, and you will give your beer plenty of time to clear itself.
Yeast only affects the taste of the beer if it's in solution, if you shake it up when you pour it. The proper way to pour ANY bottle conditioned beer, be it commercial or homebrew is to "Pour to the shoulder."