I agree that “swimsuit” is more natural for American English. I’ve never really heard “swimming suit” used before, but I have heard (and often use) “bathing suit” instead!

In the UK, we call it a swimming costume, hehe.... or bathing suit.

I would say both are native, but swimming suit is very old fashioned. In New Zealand we say swimsuit, but in general conversation they are referred to as 'togs'.

I would say for American English "swimsuit" is more native. :)

'Swimsuit' is definitely the most common and natural term. Other, more old-fashioned, terms are 'swimming costume' and the very outdated 'bathing costume'. I've never heard anyone say 'swimming suit' - you can probably forget about that one.