You cannot connect any bluetooth controller to the 3DS. 3DS doesn't have bluetooth connection.

You actually can't as of now but some homebrew dev may do it soon knowing the modding scene for the 3DS family there is most likey going to be one for the new 3DS family if anything

Luma3DS has an input redirection feature that lets you use external controllers on a 3DS, but you'll need a computer and an Internet connection. I've used it on an Old 3DS XL, but it should work regardless of your 3DS model!