How to get a Bright color Sampled as RGB in CMYK?

I made the mistake of creating a design in a document as RGB, where I used a bright blue color which is the one I showed the client. She liked that bright blue color, but now the problem I'm facing is that I need to send the printshop a PDF in CMYK, making it imposible for me to find the same bright blue in any CMYK pallete.

Bellow is the original RGB I showed the client

This is the closest blue I could get in CMYK

Any help will be appreciated