IF you want it blued, I have been very happy with Loren Fogle's work.
Fogle's Gunsmithing.
His prices are, I think, less than $300, and that includes disassembly and reassembly.
He no longer does the High Polished finish, but the pistol below is one that he completed in High Polished Blue for me, before he stopped. It may look more of a satin, but it is really a brightly polished blue.
I have also had him do the Satin Blue finish on a Star Model S Super and Star Model F.
Now, I will be honest. I have always detail stripped the firearms, sent them in, and then reassembled them. This gets a discount. I think 20% off, IIRC.
Since I would do this anyway to verify and clean, I went ahead. That made the work on the Star handguns worth it to me.
Bill is right- bluing is not the best finish.
Yet, it is a nice finish if done well.
What I am looking for now is someone to rust blue a '47 High Standard HD Military, but not charge an arm/leg.
My 'carry' firearms get cerakote, hard chrome or nitride.
My range toys, that will NEVER see a holster [case to gun rug while loading, shoot, gun rug, clean, case] I like blued steel.
Yet, it isn't as durable- that is for sure.
good luck with the decision.