Depending upon your location, $118 is within the going range for oil changes, if they use synthetic oil (~$5-6/qt).
But here's something to consider since you are a new e39 owner and currently not a DIYer. Buying a used e39 is quite affordable. Not so much, maintaining this car. The cost of e39 maintenance can be exhorbitant if you pay for ALL of your service. This forum is an excellent resource for troubleshooting issues (so that you don't get ripped off) and helpful DIYs for many maintenance needs of your car. The e39 is one of the last cars that people can actually perform maintenance on. Even if you have never ever picked up a wrench, I would suggest that learning to do so would be extremely gratifying and cost effective. Even if you just did simple things, like an oil change, you could save hundreds of $$ that could be put towards other maintenance that you would never consider doing.
For an oil change, you do not even need to get UNDER the car. For a $50 investment, you could buy a Mity-Vac and suck the oil out of the dipstick tube. The oil filter is right on top and takes 5 minutes to replace. Add 7 quarts of oil and you are done. The entire process can be done in 20 minutes.
Whatever you choose, good luck on the "new" car.