Yes, but you call her bluff and tone down the wager.

At first you feel like the cosmos has granted you your every juvenile fantasy in the one package that is Selina Kyle and this challenge. It is very, very tempting to say yes. However, you're no longer a teenager and you learned along ago when you feel like you're being bullied to always call the bullies' bluff, no matter how alluring and beautiful they may be.

“How about this.” You cross your hands and go into doctor consultation mode. “I agree to the wager about the Athenaeum, but not the other payments or the money. If you win, I agree to take you to see the English jewelry collection. If I win, you allow me to take you on a date of my design. That's it, nothing more.”

“What?” For the first time a confused look comes across the usually confident Miss Kyle. “Are you gay?”

“No.” You chuckle. “I'm very much into women, especially someone so physically stunning and intriguing as yourself.”

“Do you have some disease then?” The emerald eyed enchantress is completely nonplussed.

Shaking your head you explain, “I've learn over the last three years to savvier every stage of life and one of the most pleasant is the honor of first getting to know someone. I do not wish to rush that, especially with someone as yourself.”

Struck silent, your date simple stares at you.

“I realize we only met a short time ago.” You contemplate out loud, “And I don't know why, but I feel that you're a much better person than you give yourself credit for.”

Kyle's eyes go wide as she blushes while looking away. “Damn,” she whispers and then looks back at you, her visage changed as if some facade has been removed.

“Alright, David.” Selina nods, “You've got yourself wager.”

Taking out your phone you punch up a poker game app and place it in the middle of the table in between you.

“One game to decide the winner.” After pressing “begin” you look up at Selina and smile, “Ladies first.”