It takes a certain bit of finesse to woo a mature woman. They're impervious to most of the cheap tricks and stunts most men are used to executing. So how can it be done? Can it even be done to begin with? Of course! Whether she's only a few years older or twice your age, there are legitimate ways to attract her attention...
BE GENUINE. This is the most important part, because any older woman with her head on straight is going to detect your B.S. straight from the gate. When you approach her, don't go too formal or too casual. Play towards your strengths. At least you'll know whether she accepts you or not upfront.
MAKE HER FEEL YOUNG. This can be done one of two way: directly or indirectly. Try downplaying her age in a clever way, like pretending that she's too young to drive or something along those lines. Tailor it to whatever the environment is where you meet her to make it more effective.
COMPLIMENT HER MATURITY. This one's tricky. Say something like "I don't like younger women, they don't know what they want and play a lot of games." Find some kind of way to basically say "older women are better" without making her feel too old.
TAP INTO YOUR YOUTH. A good deal of older women are attracted to the youthfulness and vitality of younger men. So run with it! Don't be afraid to say things that indicate your age, she may like you more for it!
HAVE AN INTELLIGENT CONVERSATION. If you seem like you're a little older than your years, she might like that too. That means you should pepper your flirtations with things relevant to people a little older than you.
COME OFF AS A STUDENT. Imagine that one teacher you had the hots for when you were still in school (or while you still are), and think of how you would approach her. Some women like to be a little dominating, in the fact that they have more experience than you in some areas. Approach her as if you have had some experience, but are willingly to learn more, and she might bite.