This is a great case for using BCC (blind carbon copy).
This article quotes a business school professor explaining its use:
“Moving you to BCC,” Argenti told me, is essentially a shorthand for saying, “I know you really don’t want to hear this, but I do want you to know that we’ve gotten in touch, and thank you very much.” Bim, bam, blessedly silent boom—politeness all around. It’s so elegant. It’s so merciful. And a similar approach can be used when a conversation that started with many people has narrowed to require input from fewer participants.
So whenever you are sure that the other recipient(s) of an email don't need to be on the list anymore, you can go ahead and move them to BCC. (It sounds like it would have been appropriate for Gary to do so in his reply to you, but it's easy to forget or overlook.)
This blog post gives an example of how one might use it after being introduced to a new person:
However, you also don't want to remove your colleague from the thread without notice. Then you leave them wondering if you ever followed up or if you got their email introduction at all.
This is the perfect time to move your colleague to BCC, and send an email like:
Re: Neville -- Scott
Thanks for the introduction, Brian! (moved to BCC)
Neville, I'm happy to meet you. I'd be happy to move forward with ... [rest of email]
Your colleague knows you responded, which removes any lingering doubt about whether you followed up. You've also saved them from an email chain they don't need to be included on moving forward.
Sometimes people recommend against using BCC because it can seem "sneaky" (as explained here), which is why it's important to explicitly state who is on BCC.
Another example: My team at work has an email alias for users who are beta testing our software. So very frequently someone will report a problem to the list, and the engineer or PM responsible for the feature replies with something like:
(discussion-list to bcc) Thanks for reporting, Bob! Can you send me the log file?
This lets everyone know that the problem is being handled appropriately, and keeps the list from getting looped back in later if someone accidentally hits reply-all.
So in your case, instead of hitting reply-all, reply just to Gary, but BCC Bob and mention that in the first line. Then you can continue the conversation with Gary without filling Bob's inbox.