Hello and thank you for your question! My name is ***** ***** I will be assisting you.
The main concerns a woman has about giving out her number are:
Is he married/in a relationship?
Is he going to call/text me all the time?
Do I even want to see him again?
Sometimes it is better to give her your number and let her decide whether she wants to pursue the conversation further. But that leaves you in a position of waiting to see if you will ever hear from her. If you prefer to be more proactive and skip the waiting game you might say:
"I don't mean to bother you but you are very pretty. I don't know if you are seeing anyone or not but I would really like to get to know you and talk sometime. Would you like to exchange numbers?"
"Hi. My name is... You caught my eye and I don't know if I'm your type or not but you seem like a really nice woman. I've got to get to work (or wherever) right now but do you think we could talk on the phone or text sometime?"
"Hello. Can I ask you, are you seeing anyone right now? If not, do you think you might like to go to dinner or a movie sometime? I know you don't know me right now but maybe we can text or talk on the phone, get to know each other and see what we think with no pressure. The worst that could happen is maybe we both make a new friend. What do you say?"
It's always hard making the first move but say something that is natural for you. Be yourself. Women appreciate honesty and openness more than trying to figure out what a guy's angle is.
Thanks again for your question! If you need anything additional just let me know. If not, please rate positively so I may receive credit for helping you today. Good luck and have a great weekend!!! :)