Reference check post-offer

Intern in IB-M&A

I received a formal offer letter after 5 rounds of interviews with a fund after I failed to win a return offer from my past summer internship at a BB. 

I got along quite well with a few Analysts at the BB past summer. They actually vouched for me in the return offer decision making process. Not sure if they'd know I didn't get it though, and I haven't contacted them since then.

Now the fund asks me to provide a professional reference from my most recent internship beyond standard background checks. A reference checking platform will do the job by sending a few performance-related questions to referees. 

Given that I would probably have to request a reference from one of the Analysts, how would you recommend me doing to contact them and ask for favor politely?

Huh? Why is this so complicated? Also, if you are going direct to buyside these analysts may want to suck up to you if they don't have an exit yet.

"Hi Blank, hope you're doing well. I recently received a full-time offer at [firm name or type] and they are now conducting some reference checks. I had a great experience working with you last summer and learned a ton, so I was wondering if you'd be willing to act as a reference for me.

Let me know.

Thanks!

[Your name]"