He'll ask her sometimes: why don't you get a hobby, or a boyfriend. Clara almost laughs at him because she remembers all the times she would go out and then the Doctor would appear. He'd vworp-vworp into her yard, or the street, and she'd grab her things, maybe put money on the table if he was outside a restaurant, and leave. She'd toss her hair over her shoulder as she ran, saying thanks very much but I've really got to go.
So it's not like she hasn't tried.
She's got human habits he doesn't understand. Once, when they were in London, she ran into a shop to buy lotion. She rubbed it over her hands in even, rhythmic motions: up past her wrist to her fingertips and back again. He asks her why and she says that the smell reminds her of home. He doesn't know what "home" is - he's never really had one. He's had nothing but this box and the drifting universe for years longer than she's even been alive. Distant memories of Gallifrey will flicker over him sometimes, memories that make it hard for him to move forward. He'll be programming the TARDIS, or fighting aliens with Clara, and then they'll hit him: bright, bright orange light and waves of dust, rocks, chaos. Like he's living in two places at once.
It's Clara's human presence that grounds him. She's so tiny and fragile and a bit strange: she's got endless pairs of stockings, and wears those ridiculous shoes. Oxfords, she called them. They've got a bit of a heel. He always wonders if she can run in them, and she always surprises him.
He gives her a room on the TARDIS. When she asks him why, he shrugs. "Just because I don't necessarily sleep much doesn't mean that you don't need to." Clara finds herself sleeping there more than at home. It's easier, she tells herself. Easier than another night spent coiled, waiting, bags ready just in case. When she is home, she's tense. She snaps at her students and fumbles through dates. Her mind is always halfway through the universe, wondering what adventures she's missing.
It's not just the adventures, though. The Doctor is a presence that intrigues her. She daydreams about what's going on in his head. He's quiet, serious, withdrawn: like one of her favorite novels that's just begging to be opened and explored.
The daydreams go darker, more interesting, at night. Clara finds herself wondering what it would be like with him. It's not that human boys don't have interest for her; of course they do. Clara just tells herself that they're complicated, they're different, they're far away. Really, it's that she's getting a bit tired of all the running. The pretending. It's like she's living in two places at once.
One night, she imagines that the Doctor kisses her. It's silly and stupid but she feels her whole body buzzing. When his head moves lower, she wakes, gasping.
For days after that, she can't even look at him. He doesn't seem to notice a difference; he just teases her and insults her hair as usual.
The awkwardness thaws out, though, and she loosens up enough once he teaches her to program the TARDIS. She learns that it's as much of a mental connection as it is the physical process of beeps and levers. "It's about trust," he explains, and that's when she realizes that it's the same kind of relationship she has with him. It's a closeness she hasn't felt with anyone in a long time. It makes Clara feel a distant ache for what could have been. What that looks like, she can't even define herself.
She stands there, at the console, feeling a little sad and out of it. In the haze, she must've pressed something wrong because the Doctor is now behind her going "tsk, tsk," and then he leans past her shoulder and, hand over hers, slots the tab into place. "Like this," he says, patient for once.
Clara turns around and faces him. "Teach me," she says, like it's some kind of dare.
Really, though, they end up teaching each other. She guides his hand up between her legs and over her underwear where she's already so wet that she's half-embarrassed.