What should I do about shy guy who might like me?

Asked me to drink a couple times,started to get close but I got scared and things simmered for a while, now hes texting me again. One day we talked for like 5 hrs thru text. He texted me or showed up to where I work every day since then. But he hasn't asked to hang out again. He was asking me a lot for a while there but I couldn't the last couple times. When we texted that one day for 5 hrs after i thought the convo had ended he said he was bored..like a hint to hang out. Should I ask him to hang out sometime? without it coming off as asking him on a date? Are girls expectd to make the moves too? Or is he supposed to? He always did make the first moves before.