You two have been dating for weeks, and Bob has no idea? This can only happen in one of a few ways:
- you're dating secretly, and nobody knows. You don't go places together in public, you don't mention to your friends what a great time you had [at the movies, on a picnic, at the zoo, at that new restaurant] with your girlfriend, Alice, on the weekend
- You and Bob are not that close, so while you tell many people these things, you don't really see Bob to tell him. Ditto for Alice.
- You are actively hiding the relationship from Bob because you're worried how he will react
If it is the last, then I think you are missing a third possible reason Bob might get angry, which is deception and hiding.
I presume you don't want this to be a big deal and don't want Bob to be angry. So don't make this into a big deal by sitting Bob down to tell him. Just start mentioning this aspect of your life whenever you talk to him, and encourage Alice to do the same. Work it into an ordinary conversation.
Oh man, last week I went to [thing] with Alice and it was amazing! [Details of what was great about thing.] You should totally go if you get a chance!
[If Bob invites you to something] That sounds terrific! I need to check with Alice to see if we have plans that day already.
[If Bob tells you about something he did that sounds fun eg a movie, an art exhibition, a new restaurant] I wonder if Alice would like to go to that with me. It sounds like something she would really like.
Alice should be doing the same when she has her own conversations or get-togethers with Bob.
While he might ignore them, any one of these comments could easily lead Bob to say
Alice? What does she have to do with anything? She's my friend, after all.
(Or the equivalent sentence to Alice about you.)
At which point you can say something like,
Yes, she is your friend, and we've been on several (a few, a lot of) dates since a few months after you introduced us. I'm so glad you did!
Don't rush into a summary sentence like "we are falling in love" or "it's getting serious" or "it's time to tell people we are a couple". Let him ask you that sort of thing.