If you transfer (rack) your beer into the glass carboy, do you have a racking cane? It's a long stiff tube with a bend at the top.
Racking canes come with a little plastic cap that covers the bottom opening of the tube. This little plastic cap will filter out some of the bigger particles when you rack into your carboy.
Unfortunately after racking, you should rinse out your bucket that has the spigot and rack back into that from the carboy. It's much easier to bottle from something that has a spigot.
Your beer will still develop little yeast cakes on the bottom of each bottle but when you pour the bottles into glasses leave the last bit with all the yeast behind.