What should I do!!!?? HELP PLEASE (I LIKE THIS GUY)?

I like this guy and would like to get to know him a little better without making him think I'm trying to flirt with him, (even though I am) he just seems kinda shy and akward, and I'm very shy and akward myself so if I tried to flamboyantly flirt with him it would just be super akward, not only that I don't want to come off as easy or anything. And I do think he likes me, but he's seems really cautious about it . He's also kinda older than me if that matters. Anyway any advice? I don't mind reading long answers. (We work at the same hospital, not school)