Yes. If you file a tax return, you have to report all your income. The money you won at bingo is gambling income and has to be reported.
(If the $1,036 from bingo is your only income for the year, you do not have to file a tax return, so you do not have to report the winnings.)
Maybe you are thinking that you do not have to report the bingo winnings because New Hampshire has no personal state income tax. But you have to report all your income on your federal tax return, no matter where the income is from. If you live in a state that does have income tax, you have to report it on your state tax return as well.