If you think a little, what is wrong in that? Will the woman wait till the man has the initiative? Maybe he is not a good observer or just shy, afraid of rejection. Many men seem to be independent and strong but in fact they would like a woman by their side who knows what is best for them and appreciate their efforts. Everybody needs to be encouraged, even those men who are self assured and always in control.
If you are a woman who feels too embarrassed to be direct and ask a man to a date, you can do something else, like initiate a discussion or small talk about anything. Do not be surprised if he will ask for a date at the end of your conversation.
If after the conversation you are satisfied and have things in common, settle a date - do not be in a hurry, anyway.
You need to consider this: be yourself and do not flatter him. You don't want him to think you are a flattering bimbo. Don't exaggerate with compliments, laughs at silly jokes and don't let him do all the talking.
You must understand that not many women make the first step, so give him time to appreciate your initiative. Tell him you will call and do it. You can settle a date in a public place.