Hi Janis, I'm still a novice with tanks, so please bear with me! If you haven't already, you could try looking into the cause of it, the most likely suspects being too much light and food/wastes. Try reducing it, along with smaller more frequent water changes for a time. Make sure there's no dead fish lurking somewhere that didn't get removed. So basically speaking, starve the algae. Was there a recent cause that you know of for the bloom or had it been an ongoing problem?
As to your question about Bamboo shrimp, I would only get them if you thought they would be an interesting addition to your tank (I think they are, but that's just me). They can live quite a long time, at least 5 years according to this site, so they are not for the shorter haul. Another potential problem is that if you happen to have a community tank, it is difficult to directly feed them. For example, when you swirl finely crushed food into the water, the fish will end up getting most of it. Some people do keep them with fish; I'm just mentioning that this problem does come up for you to consider.
I do think Bamboo shrimp will help filter the algae from the water and as to eating enough, just like the smaller shrimp, they can eat a lot when they've a mind to, but that also means they'll poop a lot (yes, it's and endless chicken and egg cycle!). You'll probably need at least a few or more for a 77 gallon, but again, I would also try to control green water by reducing the cause.
I had two Bamboo in a 10 gallon (which is too small) and they kept the water crystal clear. They've very recently been moved to a 5-week old 20-gallon which has a mild case of green water by the way. However, they went nuts with the light coating of algae on everything and have been using their secondary method of feeding, which is "sweeping" their fan on plants, etc, to get at the food. They've only just begun to "filter" so don't have your answer just yet as to their impact on green water

. But I'm fairly certain the water clarity will improve, though part of it will be the tank maturing, I think, and the fact that the only other inhabitant at this time is 1 Zebra Danio. This tank gets a lot of natural light though, which will be a battle in the making.
-GB