If the shop you took it to couldn't diagnose the issue, I'd try another shop. There's clearly something wrong if your dipstick is dry after only 250 miles, assuming you're warming up the engine first, waiting 5 minutes or so, then checking the dipstick while the car is on level ground (the oil check procedure is described in the owner's manual).

My experience with valve stem seals was similar to those mentioned above. My X used a quart roughly every 800-1000 miles. And after sitting at a long stop light, or sitting in traffic, or sitting in a drive through, I got a big puff of blue smoke out of the tailpipes. But without the idling, there wasn't really any noticeable smoke.

$12k to repair the valve stem seals probably includes removing the heads. There's not much of a good reason to do this anymore now that AGA came out with a tool to allow the seals to be replaced without removing heads. Cost on this repair should be about $2000. Yes, it's not cheap, but it's way better than $12k. When I was shopping around for my repair, most of the shops in my area used this tool. I bet yours would too.

Also, I see you're in NJ. There's a guy who does this repair for about $1500 in NY or NJ with lots of happy customers. Search around here and on other BMW forums - he's mentioned a lot.

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2006 X5 4.4i
Sport package, summer package, cold weather package, DSP + Nav
Bought 2/14 with 73k miles