These are reportedly the best type of texts to send ex's when you want to re-establish contact with them, or at least this has been argued by Michael Fiore (I think I have his name right).
The nature of a Across the Bow text is that you are messaging them without being needy, without begging and without desperation. You are opening channels of communication and without pressure for them to reply.
An example of an Across the Bow text would be..
I heard a song by Nirvana earlier, it reminded me of how we used to listen to them . I hope you're doing ok.
To me, that text says... I can't stop thinking about you, wanted an excuse to text you and by not asking you any questions I've given you a way out of not actually wanting to reply to me. I can't stop thinking about the times that we shared together and want those times back now.
In short, it says all the desperation and clingy stuff but in a not so well wrapped guise. And then, if she chooses not to reply then it's done with.
Not a great style of approach, I think it would only work if they were desperate to get back the relationship but didnt want to lose face.