For me the first and foremost is for the shop to be able to supply the parts I chose not to force me into whatever their supplier is selling, what they typically use or OEM parts just because it's easier to source. I'm keen that way because I like to use parts from OE suppliers (exact same part) but at a fraction of the OEM cost. I do my own research to find the parts and shop around to see where I can find those specific parts and at what price.
Second, I would expect not to pay more or much more (few bucks higher is acceptable of course) over the LOCAL RETAIL price for the same P/N (e.g. Germanparts.ca, shop.bmw.ca). If the shop can source the exact part at lower price from their supplier (I hope so and assume they do) by all means, I would not object them sourcing the part and sell it to me at RETAIL - I would not expect any additional discount on the parts. For me, Germanparts.ca is kind of the benchmark when it comes to German cars parts sourced locally. If they have the part in stock, I pick it up the next business day so delivery is fast.
Now, if the gap between the LOCAL RETAIL prices and Rockauto for the same P/N is significant - in hundreds of dollars (like it was for the A/C compressor for the BMW), I would like to have the flexibility to bring in my own part. Yes, I fully understand the warranty risk is on me, I may not benefit from labor rate discount and that's absolutely fine by me and totally fair. What I would expect though is not to be gouged on inflated repair time to make up for the eventual profit loss on the parts. I would not find this fair. It takes the same time to install the shop part or my part. The part is in the trunk by the time I drop off the car so no waiting time at all.
I typically have a before hand understanding of what's involved in a repair and how long would it take roughly (I do my homework ahead of time). Of course, there are odd cases, especially when dealing with rusted suspension bits on old cars, when a repair can take longer due to seized bolts and such. I know that first hand (did 4 brake jobs this summer on 8+ years old cars) and I can fully accept more labor time in those particular cases. Under the hood not so much as the likelihood of rusted bolts or complications is much lower in general (on my cars anyway).
BTW: Just replaced the left washer nozzle on the BMW yesterday with a Vemo part (OE manufacturer). Side by side, absolutely identical with the OEM one down to the color of the rubber gasket (green). Vemo part $62 from Rockauto, OEM part $125. Few days ago I replace the stop/start button with a WVE part (OE manufacturer) and same story - this one even had the OEM logo stamped on it. $95 at Rockauto, $145 OEM.