How do I say "I'd like to transfer cash to Y account"

(I'll be walking into the bank with cash, and want it transfered to someone else's account)

my best guess . . . after walking into the bank and meeting a clerk . . .

อยากส่งเงินสดไปเข้าในปันชีของเพื่อนคับ

The phrase you said sounds fine, although i'm sure there are other ways of saying it. You won't actually have to say anything though. You just go in and pick up the deposit form, some bank have a deposit (no book) slip. Fill it in with your friend's bank account details etc and take it to the cashier. Perhaps you should be prepared, in case it's a rather pretty cashier. Then you could have some flirty phrases ready.

I showed up to the bank . . . there were like 5 different forms and I really didn't know which to use or how to fill it out . . . so I walk up to a lady and say

"อยากโอนเงินระหว่างบัญชีของเพื่อน"

then followed it up with a

"่ทำอย่างไงดีครับ?

And after a few questions from her, she filled it all out for me. Success! But . . . I didn't even get her name

จีบไม่เก่งรึเป่าว่ะ?

Closed per OP request - double post.