Highly disagreed. If he were trying to talk about work, studying or the weather, then I would agree. His
texts are on the fun side of things. She would look forward to hearing from him.
After not being in communication with her for a long time, he needs to build up rapport again. If anything, I think he jumped the gun too quickly on asking her out. Building rapport through texting can be done, but it takes a bit more time.
His texting style is very similar to mine. It's very light-hearted and fun. There's no way in hell she's bored with his texts.
OP, keep in contact with her and keep the conversation fun. Try to add a bit of flirting into it. Do it for about a week and try asking her out again. If you get rejected again, then cut contact and move on.