It's about 20 minutes to the airport depending on whether your driver is in a hurry or a BIG hurry. If you arrange for the taxi through your hotel and pre-pay the hotel, make sure that someone explains to the driver that you pre-paid.

Did UA put up a sign at the appropriate entrance at the terminal? Seems to me I was looking for one the last time, couldn't find the UA sign, and just wandered in. It must have worked out, since I recall being in the lounge in about 10 minutes.