I often do that. Unfortunately, I rarely get a response, but I understand, tough.
When I am on the lookout for models, I tend to do in the the right groups (photography, modeling, fashion) and in my region to make the shoot easier to schedule.
My general rule of thumb is to charge a certain amount if I am asked to shoot, and to a trade shoot if I invite first. However, if I invite someone for a shoot and that person asks me to travel more than I can apply for a trade shoot, we negotiate a small symbolic price to compensate. Nothing expensive, tough.
Why do experienced photographers sometimes do this random invite? Well, I can tell for myself: we often look for people who we deem they could do well as model, so we like to try and have that experience.
Some photographers have more experience in boudoir, others in beachwear, others in casual / street, and so on. And we usually try to have new additions to our portfolio with themes we may not have so much. Example: I have quite a few boudoir shoots, a LOT of belly dancers shoots, a bunch of casual / street, and a few artistic nude. This last theme is one I would like to grow, but due to its nature, its hard to find models for it (so thats the only theme I have more at fault in my portfolio).
If a photographer invites you to a photoshoot, ask around, try to get in contact with people who worked with him before. Also look around his website or social media. And ask him what you need! Really, ask him what you want. I insist my models ask me stuff so I can clarify them of whatever questions they have. Can they take a friend with them? Always, and I encourage them to. Can they know the place for the photoshoot beforehand? Sure, I never leave my house without knowing first where are we going. How long does the photoshoot takes? Depending on the place, outfit/s, and distance, we can take 2 hours up to 3 or even 4, if they have the time for it. But I usually ask them if they have any time limitations so I better organize the whole shoot, from starting hours, to finish.