I didn’t read through every comment here so I apologize if I’m repeating someone. The simplest thing you can do is to do is informal market research in the form of a Google search for other trainers in your area and see what their rates are for the same service. Once you know about what market price is, that will tell you what people are charging and if there is a market of people out there willing to pay it. It will likely be a narrow range.
From there, you can try to compete on price by undercutting them slightly, but I wouldn’t do that. Try to differentiate enough in your service from what others are doing so that you can convey the value of what you do easily to potential new customers. If you really want to cater to each client’s needs thoroughly, you can charge the very upper limit. Like a “luxury” service or something. Sometimes by doing that, you can increase the perceived value of what you have to offer in a prospective client’s mind.
Whatever you decide, be sure to figure what you need to break even and profit as being mobile can eat up a lot of time and resources.