This sounds like a really scary cram school in worn down building in a back alley. It could be a very legitimate school, but the name scares me. I have never heard of it, though, so I will add that this is only my opinion of the name.
I will chime in about bilingual schools, since I always rant about them on this forum: Taiwan’s definition of “bilingual” school is “a school with some English instruction in PE, art, and music”. It usually involves throwing a white person in the room who may or may not have any idea how to teach, while calling the local teachers who may or may know any English but do all the teaching “assistants”. If it is a public school (I’ve been to about 11 “bilingual” schools around Taiwan and 2 in Kinmen), no academic classes are taught at bilingual schools and the students are barely at level in their English ability (compared to what the government-issued textbooks expect of them).
So be very careful about the use of the word “bilingual”. Find out what the classrooms look like. Look at the textbooks, especially the English ones. Make sure any supplementary English text makes sense and isn’t teaching crap like “x” is for “x-mas”.
Ask to speak to the principal in English. If they can’t speak English, walk away. You can’t run a bilingual school if you can’t speak one of the target languages. If the principal’s English sucks, there’s a good chance that focus is on the $$$$$ and not the English proficiency.
If you can, go in person and sit in on a class. Decide for yourself if you think the environment is good for your kids.
But if your kid already speaks both languages fluently, I’d send them to a local school. They’re more likely to get to know local friends and learn Chinese naturally. Plus, if you want to stick around for a few more years, they’re going to need the intense, mind-numbing academic environment that is the Taiwanese school system.