I can't say for sure on that car but I will give you my experience for reference.
One month ago I bought a 2002 330CI Vert with 80,500 miles on it. I paid $8,300.
So far I have had to do the following to the car.
1. $150 detail, as the interior was very dirty, only one rip in the leather the typical on the driver seat bolster.
2. Bout a 6" gash in the top where someone knifed it. Got an upholstery shop to patch it for me for $50. Looks okay and got rid of the wind noise.
3. Replaced temp sensor.
4. Replaced FSR, as AC fan was not running smoothly, works good now.
5. Power steering resevoir gasket.
6. Valve cover gasket.
7. New shocks, went with a coil over kit.
This is what I have done so far. Needs some more work. The top of the engine looks clean as a whistle, the bottom is covered in oil. Thinking my OFHG is bad. Also I have a squeeky bearing in the front. Also my driver side batwing is destroyed, gotta do a repair there. Oh and the chrome wheels are nasty, pitted like mad, either need powdercoated or replaced.
Now, I give you all this info to say this. The car ran smooth, drove great and shifted smooth for the 20 minutes I test drove it. He was asking $8,900, I tried for $8k and ended up at $8,300. I am still happy with the purchase. I have done all the above work myself so I am only out the cost of parts. If you are going to do everything yourself like I am then I would not be worried about a 112k mile car if you can get a good price. I would not pay close to their asking price for that car. Too many miles. And I don't know how well you trust your mechanic but there are lots of things that need attention on a car this old. Has the cooling system been refreshed? That is next on my list. Even just the small stuff I have already done can add up in parts cost.
I would start at $6k for that car if you are comfortable with the car. Mine had 32k less miles and is the better 330 and I got it for $8,300 so I don't think you are out of line to start at $6k and see what happens.
2002 BMW 330CI Convertible