Bluegrass, if well-fed, would repair itself over time, but you may not wish to wait. In the Bay area, you may not need to if July weather isn't hot and sunny (I understand that "area" can be a rather widely interpreted word...)

If summers are pleasant, you can reseed as soon as the nitrogen flushes out the soil. You can do that with three or four inches of water, or wait for nature to supply it, in the areas that are burned (areas that are not burned are doing just fine and don't require it).

Post that, scalp the dead grass, scratch up the soil a little, and seed into it. Water just that area two to three times a day to keep it damp until you get full sprout (fourteen days for most fescues and ryes, thirty days for bluegrass). Then back off to once a day watering for two weeks, once every other day for two weeks, once every third day for two weeks, and so on, until it works with the rest of your lawn and goes deep and infrequent.

For the first year, it may need a bit more watering, but the area is small enough to do with a watering can.

If your area does feature hot July and August weather, wait until August when summer starts to break a bit for fall, and seed at that point. Just a few hot days can really do a number on young grasses, and it's better to wait a bit than have to do this twice.

Appreciate the advice. You’re exactly right about the weather being so variable in the “area.” Although we got up to 85-90deg during Memorial Day weekend, it should be about 70-80deg on average through the summer. So perhaps I’ll re-seed once I flush the area.