How do I go about asking an older woman out?

Workplace romance is generally a BAD thing in all occupations man. Be cautious.

That said though... just talk to her, see if she has any common interests with you, for example... as random as it may be, say she talks about Renaissance Fairs... plant that in your head, and then say one comes to your City the next month, say "Hey Jane," (replace Jane with her name obviously), "there's a Ren Faire coming to town next month and I was gonna go check it out. You should come."

That way you're telling her she should come instead of giving her the power to reject you if you just ask. It's more confident as a man this way.

Just be your natural self, and nonchalantly ask her out. Don't overthink it, she's just some woman right now. And you are giving her a chance to come into your life. Yours. And you should be the most important person to you. Man up and don't fear rejection.

start out slow and say hello ---- ask her for a coffee outside work