My leasing agent sent me a bill for commission he would have received if our deal went through. It didn't..

If you have no written agreement then you have no obligation. Call the agent and thank him for his time and tell him you will work to send referrals but cannot pay since the transaction did not close. Normal listing agreements and tenant rep agreements do state the commission is owed when the lease agreement is signed. Did your partner sign any agreement? Was there a meeting of the minds that you would pay if the agent found you space?

It is common practice for a commission agreement to include a clause stating that a commission is due if a broker finds a "ready, willing, and able" buyer or tenant for a space, even if the owner backs out of the transaction.
However, if you have no commission agreement in place it sounds like there's potential for a "he said, she said" scenario regarding your agreement with the agent. It sounds like you should consult an attorney.

If you are a broker why didn't you protect yourself with a listing agreement that covers these exact situations?
A broker/agent is compensated on "specific performance" and being "the procuring cause of sale." That agent should have known better to invest 7 months of time without a listing agreement specifying how they are compensated. He's now known as an unpaid volunteer with a better education. You owe him nothing.

Most representation agreements have a clause that states a commission will be paid if the buyer/lessee backs out. I have them signed before I represent a client in the market and have been compensated in the past when a deal that was negotiated failed. Did he diligently work the deal? Was his expertise helpful to the deal? If the answers are positive then you should consider paying him. My bet is he will negotiate the fee to a reasonable level with you and you will retain a business associate for the future when you pick this up again. It's good business.

Well that's a crappy situation, and one which your agent didn't handle well at all. There are lots of times where I'll work without a signed representation agreement, but usually those are deals that I know will close quick. If the deal starts to take too long for whatever reason, then I'll let the client know that I need to be protected. Generally speaking, we should always have a representation agreement in place before we start work, but there are times when kind agents who earn a lot of repeat and referral business will work without one. It's generally a sign that the agent is honest and hardworking; that's not to say that it's smart to work without one.
In this particular case, the agent spent lots of time and effort putting this deal together only to have your partner bail on the deal. That's very aggravating to agents. In his mind this deal was done and the money was already in his bank account. I can certainly understand that frustration, however I would not have handled it the way your agent did. I would have first contacted you for a lunch meeting and addressed the situation over lunch. I would have explained that I worked very hard without a contract because I had extreme faith that this deal was going to close. Etc, etc. You get the point. The agent shouldn't have just sent you a bill, although it's clear to me that he should be compensated somehow someway. Ask yourself this: did the agent do a good job of staying in touch with you? of explaining the terms? of negotiating the deal? of finding the space? of arranging tours? etc? If so, then I would suggest you throw him some kind of bone out of courtesy, but I wouldn't pay him the commission he would have received for a couple of reasons: 1) he didn't have a contract in place and he should have for the amount of time he put into it (teach him a lesson), 2) you don't know what the commission agreement would have paid him, and 3) he handled this whole billing scenario very poorly.
Hope that makes sense.