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If you did everything right before getting her number, you generated some attraction (I am assuming you did, or else you would not have that number) AND a bit of comfort, so that she remebers you and knows that she wants to spend some time with you, since you already showed you are a cool guy to hang with and all. It sounds to me as if that is your problem.
You are devolving into senseless chatter with your texts, and that is not good, since you can fuck up way more things than you can do well via text. Ideally, your texts should be goal focused (e.g. hey, I really had a good time last day with you... I am going to do XYZ on tuesday evening, it would be a pleasure to see you again) and that's that.
And yeah, it is quite normal you have to contact them first. You are the man, you lead the interaction.
See I actually think the OP may be getting 'courtesy' numbers... IE: if he is consistently being shot down via text and told that the target is busy, he is NOT generating enough attraction when actually getting the number... Easier to give up the number and reject via text than do it in person.
I would suggest really trying to connect when you get the number. Learn something about them and make them laugh (leave on a high note)... then when you reconnect with your text a few hrs later, anchor back to the joke you made or the high note you left on.