As you said, light speed (for any matter observer) means, at the same time, infinite speed (for the massless quanta that shape the observer’s POV).

So anything that appears to be propagating at the speed of light feels that no time elapsed. It feels instantaneous (from its POV).

But this fact renders any kind of Faster Than Light travel or communication impossible.

If matter could ever reach the speed of light, it will also feel what photons experience at that speed, and that is instantaneity (or "infinite speed", if we try to visualize this concept from a spacetime POV),and there's no way anything could be quicker than instantaneous.

So, the idea of Bob meeting with Alice before she can see the transmission he sent her is, again, impossible, because it would break causality (or instantaneity, from the POV of the transmission carriers).

Bob is a material entity created by trillions of interactions taking place at the speed of light as well, so there's no way for him to outrun the information exchanges that create his own structure. He would not be able to maintain his own physical integrity if he could travel over the speed of light.