well, being a real Mugen kit, its urethane iirc, so fiberglass will not stick to it. you are going to need to use a two part adhesive. I'd recommend going to a body work supply shop and having them hook you up with something. There is a 2 part system out there that basically mixes into urethane in a tube.
This stuff will load into something similar to a caulk gun (you'll have to rent/borrow it from the shop) Then you can just lay a bead on the inside to repair the crack. Flex it a bit to work the glue into the joint, and then you can just sand it flush when it sets up. Remember to use a block behind the paper to keep the kit smooth.
You could also try plastic welding the bumper. Use a soldering iron to slightly melt the inside of the bumper along the crack, and allow it to flow back together.
If the kit is fiberglass, you will want to get some fiberglass cloth. If the crack is not too large, you can get a fiberglass patch kit at Walmart or your local auto parts store. You will want to cut a piece of cloth (or 2, maybe even 3 depending on how strong you want it). Then mix the resin as per the instructions. You then dip the cloth into the resin mix, and press it into the back of the fiberglass. You can also use resin jelly. Its a lot thicker than the regular resin, and kind of lays like bondo.
For a small repair as this, I would just use sheets of sand paper and sand it out by hand. You will want to get a sanding block (3M makes them and are usually found in the same aisle as the patch kit), and an assorted package of paper. You will end up sanding with a lower grade paper first, and work your way up to a 220, or 320.