Question about my new friend

So i've got this stray (thought she was feral but there's no way) and she lives outside. I made her a nice cat house that's heated and insulated (threw away the one I bought and built her a nice one).

she's happy and healthy, but she's FILTHY. her head smells like oil because she runs under parked cars when dogs chase her.

Would it be reasonable to trap her and take her to petco to wash her? or would that be too traumatic?

Washing off petrol products is surely good, but it is a point only if she these situations dont happen again.

If she is still living outside and roams around, these scenario will happen again and again.

I suppose she managed to survive these motor oil happenings (and being chased by dogs too) since earlier?

So here is your answer, I think.

Good luck!