Okay there's a very hefty jump in logic that Jim makes when he starts pondering this conundrum. Because Jim is assuming that this aristocrat lady is also functioning in a breathing: optional lifestyle.

"Okay so she's way out of your league." Jim folds his arms over his chest. "Doesn't mean you can't go for it. You've gotta have confidence, Harrow. Half of being important is looking important. Acting like you belong in any setting, regardless if you do or not. You've got something on your side right away. You're not one of those rich guys that usually hang around her. You've actually done shit with your time."

Almost said 'life'. Good job on avoiding that, brain.

"Find out what she's interested in. You've traveled all over your world, seen a shitload of things. Is she into arts and architecture? Show her one of your cities. Food? The Nexus has literally everything. As for the nerves? When was the last time you were on a date? Practice human interaction. It's not hard."

Harrow's surprisingly in tact for an undead. Jim reckons that probably makes him like the hottest undead around by default. He's got this in the bag.