Okay, just to clarify, two betta can't live together, even if one is male and one is female. From your post I wasn't sure if you were asking about getting a second betta to put in their own tank next to your first betta and they can see one another sometimes for exercise/socialization, or if you want to put two together.
When they are breeding they are put together, briefly, when they are both ready to breed, then separated again. You can keep several females together in a very large tank (see female betta sorority threads for more info on that one), but those are about the only ways that betta can live together.
If your guy seems bored:
-do you have enough plants/ornaments for him to swim through/around/explore?
-some people put ping-pong balls (well rinsed) or water bottle caps into the top of the tank for them to push around
-mine like me for entertainment. I have a shiny black laptop exterior, and if I do computer work at their table and have the laptop open, they flare and argue and swim around at their reflections in the computer. Even without the laptop, if I read a book or hang out in front of their tanks, they like to come and see what's going on and seem interested in what I'm doing.
-I've heard of some people playing the radio for them (not sure how they "hear" the radio underwater, but the vibrations are what they're responding to perhaps?
-Mine seem to be interested in TV. I'm sure it's the movements of color and shapes, but they'll swim around and check it out when I turn it on.
-Some respond to mirrors (same as the black laptop), they flare at their reflections like it's another fish.
-occasionally I'll move my tanks to a different part of the house or a different part of the room. They seem interested in their new space when I do that as well.
Just make sure that your boy doesn't get over-stimulated or stressed from his new excitement. After awhile he'll probably start to try to hide, breathe heavily (if he's flaring and swimming rapidly), or otherwise seem "tired" and then you'll want to give him some space and some quiet time to hang out and rest.
Do you have a heater? How big is your tank? How often do you change the water?
Fish don't get 'bored' as such. Or depressed. People get those things.
Fish get stressed, or sick. My guess is your betta is one or the other of those, if he hasn't got a heated tank and a bit of cave or plant to hide in, and definitely tending toward the 'sick' if his water's not changed often enough for his tank size.
Then I'm guessing your fish is less 'bored' than 'cold'. And if your tank holds very little water (ie, you can fill it with anything from 2 - 16 cups of water) and only changing it once a week, he probably is sick from ammonia exposure (swimming in his own pee).
Not sure if you meant 'baby' as in he's an adult fish but cute so you just call him that or 'baby' as in the fish is actually an infant betta. But if it's a very young fish, it'll also be needing some appropriate food for small bettas.
It'd help to know how big your tank is.. then we could recommend some water change schedules to help keep him healthy.
Bettas are also tropical fish which like the high end of the tropical scale - 78-80F. So they need heaters, even in summer.. because in small tanks the temp can drop sharply on cooler nights and heat ferociously again in the morning. It's better to have a small adjustable heater to keep his temp constant that have it go up and down at room temp, unless you live in the tropics and it's not an issue.