Advice for negotiating salary verbiage?

I’m expecting a call tomorrow with a job offer (Firm A). I already have one job offer from a competing firm(Firm B). I really want to work for firm A, but so far Firm B has offered a signing bonus that would really help me with my student loans. If Firm A offers me the same exact salary just without the signing bonus, how should I word a negotiation? I understand that I would use the competing firm as leverage, but I literally have no idea how to “say” it without burning a bridge with my recruiter. Any help appreciated, thanks!

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