I have always just added liquid food coloring to my frostings for color, but it always comes out muted and somewhat runny. I tried gel coloring once, but it make my frosting very bitter! Any ideas on how to get a great grassy green?

I haven't had any make my buttercream bitter except if I put too much red or black in. I have found that powdered colors are great to get the color you wan without a lot of taste change. I like americolor also. I can control the color a lot better due to the dropper top and it seems to color a lot easier than Wilton.

If the gel color made your frosting bitter, then you put too much in. It doesn't take but a tiny bit of the gel color to dye the frosting compared to the liquid frostings. Also, Wilton colors are not as good as other brands. Americolor, Chefmaster, CK, are better.

By 'liquid colors' do you mean those little bottles one buys in the grocery store?
Paste colors have been (mostly) replaced by gel colors. They will not make your icing bitter if you don't use a whole jar
If you icing is runny you are adding too much liquid. Cut back on how much is used in the recipe; you can always add a bit more if it is too thick but it's hard to thicken icing up if it is runny.
If you give us your recipe - with directions etc - we can advise you more.

Use less coloring and I find a "leaf" green colour makes a nice grass.