Does it sound natural?

People tend to buff themselves up a bit on their resume.
(ps. I’m curious about how to use the word “buff”.)

See a translation

People tend to [p]uff themselves up a bit on their resume.

Puff would usually be said in your sentence.

Puff themselves up means you are pretending to be better or bigger than you are. Think of a chicken or cat trying to intimidate something.

Buff means muscular or large.

So when you say you want to buff up your resume. You are saying that you want to learn new skills to add to your resume.

Buff Examples.

Ex1: James is starting to get pretty buff. I heard he's been exercising everyday.

Ex2: I've really buffed up my resume since last time. I've added 2 new certificates.

Ex3: That man is too buff for his shirt. The sleeves look like they are going to rip.