should I ask the mechanic if I can bring in my own parts?

[(vikm)]

It's not a matter of trusting your mechanic as it is common practice for a shop to mark up the parts.

dad made a good comment above.

I've done this as I get a special on parts via a car "club". Usually, if you've gone to the same shop a number of times they won't have a problem. can't hurt to ask them.

Good luck.