If you are looking to fish, there's a quite a few dispersed camping areas (and many more reserved) along the Kern river. I can share with you a few specific if you cant find it. Google "dispersed camping Kern river".
There aren't many dispersed that are right near the creek, unless you are doing reserved, or first come first server.
I would head up towards sequoia on highway 99 and check them out, there's literally 10+ sites.
If you go up all the way to sequoia, you have to check if the campsite you are going to is open, some are but not.
In Sequoia specifically, there's a lot of dispersed. Also google it and you will find some. We went up to upper peppermint which is also dispersed. The creek area was closed off but there was plenty of forest to go around.
Happy adventures! Do share where you end up going.