What do you mean by "blanket of algae blooming"? Mat of slime green algae laying on the bottom? String algae? Floating algae on the surface? These are all easy to remove in that small of a pond with a minnow net from the pet store or by hand. Use the net once a week to remove stuff settled on the bottom and you will have a very clean pond.
Bio filters convert ammonia and other chemicals. They have no effect on most algae.
As Haro said, you can add feeder goldfish to produce ammonia. Some people might find that a cruel process. Less cruel, faster, easier to control and maybe even cheaper is to buy some ammonia at the drug store and put some into the pond. Its the same chemical fish produce and the bacteria eat. Or, have a beer and wiz into the pond. People are great ammonia producers too. Measure the ammonia until it gets to the level you want. Keep measuring until it goes back to zero and you know the bacteria are fully ready for fish. If you don't want to measure ammonia skip the entire thing including the bio filter. Without measurement there's no way to know if a filter is needed, or more is needed. You'd be blind. Why have a filter at all?
Or if the goal is to have goldfish in this pond I would add 3 to 5 small fish. Measure ammonia if you like, but 100 gals in a pond that has been running for awhile, shouldn't be an issue. There are dangers, most not easy to understand, but ammonia wouldn't be top of my list for 3 to 5 small fish.
UV filters do nothing once the water isn't green. Well it continues to kill bacteria but I don't see that as a good thing. Once green water is cleared it normally stays clear for several months, even several years, because certain kinds of bacteria and string algae can inhibit single cell algae growth. And the bacteria don't need a bio filter. They have been growing in bodies of water for about 2 billion years. If the water turns green again you can start up the UV again. One maintenance issue is to check the glass covering the UV light. A calcium type deposit can build on the glass blocking the light. The glass should appear clear, not frosted. This build up can occur in just a few days.
Building filters is a fun hobby, which I enjoyed for many years. But be careful not to confuse the love of filter building with obtaining a specific result. The two rarely have anything in common in the hobby world.
