Need some translation advice. I’m struggling with Mika’s double-entendre.

The sentence’s direct meaning is very clear. “Since you (sensei) and I are so close, how about we bathe together?” The challenge is her phrasing: “先生の仲だし.” How do I stick 先生のなかだし in there? It’s really hard.

If nothing comes to mind (translating puns is difficult), what’s a good backup option to keep the sentence brimming with sexual energy? I’m really trying to do it without a translator’s note (her phrasing feels way too good). I’ve been at it for days now and still haven’t come on any good ideas yet.

For those who can’t read Japanese, the phrase she’s using means to get along well with sensei. However, the pronunciation is “sensei no nakadashi”, so sensei’s nakadashi. If you don’t know that one, I’ll let you type it into the search box and learn a new word.

"I'm going to bathe now..."
"But since we're so close, do you want to... come, in?"

My thoughts are the sentence has three parts, being close, bathing, and coming. The original double entendre joins being close and coming, but you could detach those and make a new innuendo that joins a different part of the sentence together, in this case coming into the bath, or coming into her. I threw together a quick example so there are probably ways to phrase it more enticingly.