There are five entities involved:
1. Alice, who has knowledge of her transfer
2. Me, who has knowledge of both transfers
3. My bank, which has knowledge of both transfers
4. Bob's bank, which has knowledge of both transfers
5. Bob, who has knowledge of my transfer
The question is, whom does Alice trust? If she trusts me, my bank, or Bob's bank, then you don't need any more proof. You just need a statement from any of those entities that documents the transfers.
If she trusts Bob, then her knowledge of her own transfer can be combined with Bob's knowledge of his transfer, and she can put those together.
In real life, the only way to prove anything to Alice without Bob's knowledge of Alice would be to use #3, my bank. This would require that the bank can produce proof that Alice trusts that includes both the sending account (mine) and receiving account (Bob's).