Delta (which appears to be Cobb's liability insurance company) has no obligation to pay Bob's claim promptly or to respond to Bob.
Bob's remedy is to sue Cobb for sideswiping his car within the statute of limitations (three years for property damage without personal injuries in an automobile accident in California) for doing so.
Delta's obligation is to Cobb. Cobb may have a claim for bad faith breach of insurance contract against Delta if Cobb seeks coverage from Delta, and Delta fails to either pay or provide a defense if Cobb is sued. But, this obligation doesn't extend to Bob.
For example, parse the quotation from the case you cite carefully, noting the words that I have put in bold:
to make reasonable efforts to settle a third party's lawsuit against
the insured. If the insurer breaches the implied covenant by
unreasonably refusing to settle the third party suit, the insured
may sue the insurer in tort to recover damages proximately caused by
the insurer's breach.
Graciano v. Mercury General Corporation, 231 Cal.App.4th 414 (2014).
The right to sue for bad faith belongs to the insured who paid for the policy, not the victim of the insured's bad driving. And, the obligation to settle arises only once the victim of the insured's bad driving actually sues or threatens to sue the insured. Until that happens, liability has not "become apparent" so the common law duty to settle, superseded in California by the statutory duty to settle, hasn't been triggered.
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.
"A claim for “wrongful refusal to settle” requires proof the insurer
unreasonably failed to accept an otherwise reasonable offer within the
time specified by the third party for acceptance.
In the OP, the victim of insured bad driving hasn't even threatened to sue, let alone made a settlement offer to the insured with a reasonable deadline for acceptance. The insurance company doesn't even have the authority to settle without the permission of the insured. A bad faith claim from failure to settle arises when a settlement offer is submitted to the insured or the insured's lawyer (typically provided by the insurance company at the insured company's expense, but for whom the insured and not the insurance company is the client) which is forwarded to the insured's insurance company for approval or rejection.
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.
This statute applies when Cobb submits a claim to have his liability settled or paid by the insurance company and the insurance company fails to do so.
(11) Delaying the investigation or payment of claims by requiring
a[...] claimant [...] to submit a preliminary claim report, and
then requiring the subsequent submission of formal proof of loss
forms, both of which submissions contain substantially the same
(12) Failing to settle claims promptly, where liability has become
apparent, under one portion of the insurance policy coverage in order
to influence settlements under other portions of the insurance policy
(13) Failing to provide promptly a reasonable explanation of the basis
relied on in the insurance policy, in relation to the facts or
applicable law, for the denial of a claim or for the offer of a
Cal. Ins. Code §790-790.3