I think this is less about your mother sharing a room with a new boyfriend in your home, and that it should be more about general safety.
After all, your mother met this man online, just a few months ago, and your husband has not met this man (and you only briefly met him once). There's a lot of potential danger out there. Some people take advantage of older widows or widowers, and you have no idea whether this particular man is a thief or whether he's the finest gentleman who ever walked the earth.
I suggest that you just tell your mom that you'd like a chance for your family to get to know the new man in her life at a slow and relaxed pace, with your mom and him staying at a hotel. That way, there won't be too much pressure (like there might be if a stranger is staying in your home overnight). After all, you have no idea if this guy watches loud tv all night, or wanders around the kitchen looking for snacks at 3 am, or whether he walks around in his underwear. Or, perhaps he is the most considerate guest imaginable, helping to wash the dishes, and showing great consideration for your family and home. There's just no way to tell when you don't know the guy. Take your time in getting to know him, see how he treats your mom in everyday situations, and hopefully you and your family will all like him as much as your mom does. Just ask your mom for the chance to find out.