Should I ask this guy out?

ok. so i really like this guy..and honestly can't stop thinking about him. he's a pretty outgoing person, but when it comes down to his true feeling i think he's really shy. we've flirted a lot and i think he likes me. he's more of a pda (public display of affection) person but i like to talk...not that im against pda im just not as comfortable. things sorta have been going slow and i feel like i should ask him out. do guys like it when girls ask them out? what should i do?