I've thought about going to grad school to get a master's degree, so I can teach ESL to adults. However, someone suggested to me that I might not be able to find a position in which I would be teaching adults, and that I may have to apply for positions in which I would be teaching children. I don't want to teach kids or teens, though, so would it really be a good idea for me to pursue this?

Look around in your community. In mine, there's an ESL school for adults. You've got to research this.

My mother is a bilingual teacher & ESL, it was a great profession but she taught children. I really dont know about adults, I guess where there is a big immigrant population. I would ask someone in the field.

I taught ESL in public schools for a year, then went to Taiwan and taught English there with various ages.

There are jobs teaching English to adults in the U.S. Many more overseas. Lots of companies want to train their employees in English. I worked for some of these companies in Taiwan.

Having a master's degree gives you a leg up on the competition. Education is always worthwhile.

College students might be another option for you. They are good to teach- motivated and make lots of progress and are smart.

Best wishes to you.

It depends on your geography. Larger cities have more opportunities than smaller areas.
It also depends on what you can afford to make there are lots of adjunct ESL jobs available. FT/tenure-track adult ed/college jobs are very difficult to come by.
If you don't want to teach kids, then don't. It'll limit your job options, but it's your choice.