How do I know if she is interested?

I have been chatting with a girl I met at a party a few weeks ago. We had a great time and decided to stay in touch, so there have been a few messages sent back and forth. I am trying to work up the courage to ask her out on a date, but there have been no promising signs that tell me she might agree. She takes a few hours to respond to my messages and, whenever I text, I realise that I am always the one initiating the conversation. If there is no interest on her part, I may be wasting my time and the sooner I know, the easier it will be to move on. Should I be pushy and text her more often?
Why not just ask her out and put yourself out of your misery instead of second-guessing why she isn’t initiating a conversation? You are creating the struggle for yourself by not being direct, and working up the courage is all that’s preventing you from finding out if she wants to meet you or not. The sooner you get that message out, the easier it will be to avoid reading too much into her silences or lack of communication. 

This isn’t about being pushy as much as it is about getting to the point sooner rather than later. Asking someone out isn’t being pushy; continuing to do it in the face of refusal is.I’ve been avoiding physical intimacy with my girlfriend because I’m afraid of being compared to her ex-boyfriend in some way. This insecurity is affecting my relationship with her, and she is starting to wonder if I’m not in love with her. How do I get over this?
Why can’t you tell her the truth and accept that you are vulnerable about something you have no control over? She isn’t the one comparing you with her ex, nor is 
she with her ex in this relationship. Physical intimacy begins with emotional openness, so try starting from that point instead.