This is the way I do it and I learned this from Uny.
I take some tincture (liquid & herbs) from my half gallon jar and squeeze it through several layers of cotton into a quart jar. Once I get it all strained I let it sit in the quart jar until the all the sediment that snuck through settle to the bottom. You're left with the tincture on the top.
Then I use a turkey baster to extract the tincture from the top and put it into my 4oz. bottles. That way you don't get any of the sediment in your 4oz. jar. Well, I'll have to take that back because when I start getting towards the bottom of the strained tincture I still sometimes get a tiny little bit of sediment but hey, that doesn't matter at all.
Just think of the turkey baster as a GIANT dropper lol! It works like a charm.