I know he's interested - how can I get him to ask me out?

I know he has been admiring from afar and when I've finally begun to notice him, we started to flirt subtly. We work together in a busy office so there isn't much of a chance for long conversations. We smile and wink at each other a lot and subtle touches as well but never really a real convo. He seems shy to initiate anything, but when we do talk he seems really happy that I talked to him. And Only when I showed signs of the smilingsubtleflirting did he start doing more of that in return.
I am pretty sure he is single and interested, as he only does this with me. How can I get this to progress more?

How can I make it easier and more comfortable for him to approach me for real conversations without seeming too eager?

I do like all the butterflies and subtlety but at the same time, I do want to get to know him more. And I don't want him to be confused about my feelings for him. I feel that he may be feeling the same kind of confusion with me.

Maybe he doesn't mix work and dating.

I would never date a co worker

It's not the 1950's .....it's common for women to ask men out on dates. I was asking guys out over 20 years ago and it didn't kill me to do it. Get off you butt and ask him if he would like to meet up for drinks after work. easy peasy.

Surf is right - avoid dating at work. For what it's worth, I've had many an inter office flirt which hasn't gone anywhere. Flirting does not always equal intent.

But if you really want to date him, then ask him out. Smackie is right about it not being the 1950's anymore. And being shy or afraid of rejection doesn't cut it as an excuse - guys are also shy and afraid of rejection, yet most of them summon the balls to get over their fear.

Depends what you want. If he's shy (as I was in the past) he might not do anything so it depends how long you are prepared to wait. Amp up the flirting a bit and see if he asks you out. If you get frustrated that he doesn't act, you have to decide if you are sufficiently interested to be willing to take the lead and ask him out, if not then you close down the flirting and move on.