How was Mercutio being bawdy about what he thinks Romeo has been up to all night in Act 2, Scene 4?

Something bawdy is lewd or obscene, especially in the way you're talking, so we're looking to see how Mercutio is being perverted, inappropriate, or sexually suggestive as he teases Romeo about what went on the previous night. Readers should be aware that much of what Mercutio says in Act 2, Scene 4 is rather crass--not at all appropriate for young children.

For a little context, recall that Romeo had basically disappeared the previous night as he and his friends were leaving the party, so Mercutio assumes Romeo went off to be with some girl, maybe Rosaline. His comments are focused on teasing Romeo about having spent all night having sex; Mercutio is teasing Romeo gently, as a friend, pretty much congratulating his buddy in an indirect, bawdy way for what he thinks Romeo had done the night before.

As readers, though, or as viewers if we're watching the play on stage, we experience some dramatic irony here: we know that Romeo has been with Juliet, but that they have not consummated their love for each other physically. So Mercutio's assumptions are actually incorrect.

Let's look at Mercutio's first handful of bawdy comments as Romeo enters the scene:

1. "Without his roe, like a dried herring. O flesh, flesh, how art thou fishified!" Here, Mercutio is saying that Romeo looks like a shriveled-up fish that has deposited its eggs, and now he looks weak and tired. Mercutio is hinting that Romeo is exhausted from having sex.

2. Next, Mercutio mentions a bunch of famous women and hints that the girl Romeo has been with must be even more fantastic than they were--based on how tired Romeo looks now: "Laura to his lady was but a kitchen-wench—marry, she had a better love to berhyme her—Dido a dowdy, Cleopatra a gypsy, Helen and Hero hildings and harlots, Thisbe a grey eye or so, but not to the purpose."

3. After Romeo gives Mercutio the excuse that he'd had to slip away from his friends to take care of some important business, Mercutio basically says, "Yeah, I know. You had important business to accomplish with your butt." Here are the words he actually says: "That’s as much as to say, such a case as yours constrains a man to bow in the hams."

4. When Romeo tries to clarify what Mercutio means, Mercutio replies "Thou hast most kindly hit it." On the surface, this means "Yes, that's what I meant." But it's also another bawdy joke; its second meaning is "you hit your target," or in other words, "you had sex."

5. Mercutio then alludes to female sex organs, calling himself "the very pink of courtesy."

Romeo joins in on the jokes, and he and Mercutio go on and on, playing off each other's choice of words and making more and more bawdy puns. The only thing that really stops them is the sudden appearance of Juliet's nurse. You can understand the puns and innuendos that Mercutio is making if you notice that he's bringing the conversation back again and again to Romeo's exhausted body.