Is it okay if I split the bill on a first date?
Why do you think you need to split the bill?
I think I don't want my date to feel betrayed, and I'd like to pay for myself.
If I get asked on a date, I also want to offer to pay the half of my share of the bill, so I think I get where you're coming from. So I think it is nice for you to offer to split the bill, it's a very modern and progressive way of thinking. How about when you ask out your date next time, possibly tell them that you also want to split the bill on your further dates down the road?
Yeah, but I hate paying for a date when I feel like I'm doing all the work.
It would be proper etiquette to always split any food bill in half with your date. Everyone wins and there is no confusion about whether anyone is using the other person for a free meal. Split the bill and everyone is happy.