Attracting an older woman
Be able to carry on a mature conversation. An older woman has probably been in the work force for many years and may be well-educated. She isn't likely to be interested in simple sentences and beer. To better your chances, be aware of current events, be well read, listen to modern and classical music. Make eye contact and speak intelligently. Find out what she is interested in, and if you don't already know much about that subject, ask about it or learn about it so that you can have a conversation. Mature women are interested in what you have to offer them. Don't assume they are desperate to get you; you have to get them.
You must have a good job, a decent income and future prospects. A mature woman isn't interested in a starter kit; she wants someone who is somewhat established and confident. You don't have to be at the top of the food chain, but you need to be on your way up. She doesn't want to support you financially, and no matter how old a woman is, security still matters. If you are a more mature man, let her know about your career, but don't brag. If you are unstable, you're unlikely to stand a chance.
Many mature women expect good manners at all times. If you need to, brush up on your etiquette and practice before approaching that mature woman you have your eye on. Holding open doors, please and thank you, pulling her chair out for her, and offering assistance in any way are usually very attractive actions to women, but especially to a mature woman.
When you are ready to approach her, smile warmly and extend your hand as you introduce yourself. A mature woman should expect a strong handshake and will not shy away. Make eye contact, ask her about herself and engage her in conversation. Be sincere. A mature woman is likely to smell a fake from a mile away, and she won't waste her time.
After the first encounter, offer her your card. She may offer hers; she may not. By giving her your card instead of asking for her number, you are showing that you are confident she will call, and that you aren't needy. Be warm, friendly, make eye contact again, smile and tell her you can't wait to see her again--and odds are that you will.