The fact that Bob contacted Delta is still good for Bob. It prevents Delta from refusing to provide coverage to Cobb if Cobb didn't him or herself provide prompt notice of the potential claim to Delta (since timely notice of a claim is a condition precedent to the obligation to pay the claim under the insurance contract) so that it could make a timely investigation of the claim and mitigate its damages. The deadline to notify Delta of the incident is a reasonable time not more than twenty days unless no prejudice results from the delay (see also here).
A timely claim is also more credible evidence of liability and damages which, in turn, increases the settlement value of the case if Cobb does ask the insurance company to pay the claim. But a lawsuit or settlement demand from Bob has to be made to Cobb, not Delta. Delta isn't an agent of Cobb just become it is his insurance company.
Similarly, in the case of the statute quoted in the comments, the key point to understand is that the claimant, vis-a-vis the insurance company, is Cobb and not Bob. ("Claimant" can be a somewhat broader term than "insured", but this is generally in more complicated fact patterns, such as where the insured has assigned a right to payment from the insurance company to a body shop under a policy covering damage to the insured's own car or under uninsured motorist coverage).
Generally speaking, a payment on a claim is made to the insured or to another person at the direction of the insured or the insured's attorney. In this context, Bob has no claim against the insurance company or any relationship or privity with the insurance company. If Emma who is insured by Amica instead of Delta hit Bob, then Bob would similarly have no claim against Delta since he has not relationship to it.