I got a fighter fish in a bowl today. Only one fighter is put in a bowl. Now I am wondering if it will get lonely. How will it mate? Am I depriving it of a companion?
I'm assuming you're referencing the Siamese fighting fish (correct me if I'm wrong.) They tend to be very aggressive, as I'm sure you know, and it is very popular to keep two of them with a separator made of plexiglas or some other acrylic see-through material. I don't think they get "lonely", rather "bored".
As far as breeding them goes, just be careful. You shouldn't have a male and a female together at all times, and preferably not longer than enough to mate. Here's a good article on breeding betta fish. Other than that, they prefer to be alone, and no, you're not depriving it of a companion. If you want to keep it from being bored all day, you can put ghost shrimp or snails if you're willing to keep those up as well. :) But that also depends on the size of the environment. I see you're keeping it in a fish bowl, which I'm guessing isn't very big compared to an aquarium, so be careful about how many other animals you introduce into your bowl. Mind that snails waste a lot, so you may have quite a lot of cleaning on your hands if that's what you decide to do.
Betta fish, which is how your fish are more commonly known, are famously aggressive. Males in particular should never be kept with other males -- one will kill the other. Females can be kept together in larger groups with care, but pairs or mixed-sex groups won't work. Don't even worry about trying to find it a mate until you're really comfortable keeping them.
Even if they weren't aggressive, the bowl itself is a problem. Bettas really need more water than the bowls they're usually sold with, and there's definitely no room for anything else. They don't need a huge tank if they're on their own, but you may have trouble keeping him in such a small space long-term.
I've never personally kept bettas and don't know offhand what the go-to references would be, but nippyfish.net looks like a good place to learn more. There are sections on how to house them and how to choose non-betta tankmates down the road, and lots of other information about their care and natural history.
Yes is is okay to keep them separate. The males are very territorial and will fight so much that one of them could end up dead. So what you're doing is right, keep Siamese fighting fish separate for their own good.
Betta fish shouldn't be housed in a bowl primarily because they just aren't large enough with the recommended minimum tank size being 5 gallons or more for a betta fish to thrive. As for tank mates, it just really depends on the temperament of your individual betta, how large the tank is and making sure there is plenty of hiding places for each to retreat to. A betta however will not get lonely living alone. Here's a guide if you want to read more on the subject and what specific species are best to live together with the betta.