"Where're you staying? I can drop by after I get off work." Because all appearances to the contrary, Rex was at work. As much as Stark's facilities were sufficient for service, maintenance or even the larger mechanical jobs, they had only minimal fueling capabilities.
Alternatively, in a less forward/creepy way (honestly, he was doing this for the bike), "or, let me give you my number."
Rex stuck his torso through the rolled down window of the town car, and searched around in the glove box. Re-emerging with a black marker and a scrap piece of paper, he scribbled down the phone number for his connection at work. "Ask for Rex," he added, handing it over.