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 He's quiet, serious, withdrawn: like one of her favorite novels that's just begging to be opened and explored.