There isn't a way to charge for a M&G through Rover unless you're booking a stay, and in my opinion, it would scare off a lot of potential clients. They'll never get to see how good you are with their pets if they never get a chance to meet you. That said, it might be worth spending a little more time chatting with the client on the phone or through Rover's messaging service before setting up a M&G, especially if you're having to travel to meet them. I agree, $50/night isn't an obscene amount (it would be high for my area, but I'm sure you've looked into the going rates in your neck of the woods).
People, for whatever reason, don't always consider the cost of pet care when they think of travel expenses, so our rates initially seem steep. They assume a dog lover will be more than happy to watch their dog for next to nothing, without thinking of the effort and time we spend. Sometimes you have to sell them on the benefits of spending a little more. For instance, I could list my futon in my spare bedroom on AirBNB for more than I charge per night for pet sitting, and people would gladly pay it. What's more, they wouldn't expect me to feed them, cuddle them, take them for walks, comfort them when they're stressed and homesick, or pick up after them while they are here. And yet, we do ALL these things and more for their beloved pets while they are away. Make sure your clients know exactly what they are paying for and why it's worth it before you make a big trek to meet them. If they understand the value in what we do, it will be worth it.