Use car insurance or bear repair costs?

I rear-ended someone yesterday. That person's car didn't get damaged much (although there were a few scratches), but some of my car's front part (mostly chasis) was damaged. I am pretty sure that the other person will get their car fixed through my car insurance. I was, however, wondering how I should get my car fixed, considering that I want to minimize my insurance premiums from going up because of the incident. Should I (a) use the collision coverage of my car insurance and get the repairs paid for by the insurance (less the deductible) OR should I (b) bear part or all costs of repairs myself without asking the insurance company to pay for any of my repairs.

My intent here with option (b) is that if I don't use my insurance company to pay for my repairs, that's less money spent out of their pocket for the incident, thus resulting in a lower premium increase. But on the flip side, if the other person calls up and asks for coverage to fix her car, then the insurance company knows that my car was also involved in the accident, and therefore may jack up my premium, regardless of whether I use them to pay for my repairs or not (in which case I might as well get them to cover my repair costs also), which makes the case to go with option (a).

I really don't know how this works, and so am torn between options (a) and (b).

Any advice on which route to go so as to minimize insurance premium increases in the future and repair costs would be greatly appreciated.

Thanks.