Do it yourself
.
Seriously, it isn't difficult. The only problem areas will be not having the right tool for the bottom bracket, and cutting the steerer if you need to.
If you buy all your bits elsewhere and aren't giving custom in that respect to the bike shop then you won't have any bargaining for a deal, so you will just pay the full labour rate for the mechanic. Any good bike shop mechanic will do this and GBs will do it. If you want somewhere closer to home then drop in to De Vers and ask Maurice as he's a good man and will have it built up, his mechanic (can't remember his name) is also good and been with Maurice for years.
If you had a bike fit then you should have a set of detailed measurements which you can give them with the bike and parts. One thing I would make sure you ask for is to have the steerer cut a little long. You can tweak saddle position with height of post or back and forth on the rails, you can tweak reach with different length stems, what you can't do is add a bit back on to the steerer if you cut it too short. Best bet is to cut a bit long and set up with about 20mm spare spacers on top of the stem. Once you are sure you have the position right and don't need to change or move the stem you can get it re-cut to a closer fit. Always have it cut with 5-10mm on top as some stems are 35mm deep and some 40mm deep, so if you currently have a 35mm deep stem then you want to make sure a 40mm deep one will fit should you change at a later date or you reduce your options.