How much per month will a 1 bedroom apartment in Bowery, New York City cost?

The Bowery is actually quite expensive now. A lot of the buildings are luxury high rises that have one bedrooms starting around $3000 / month. You can try to find one for less but I doubt you'll get one for less than $2000 / month because the neighborhood is so trendy. A lot of people live in studios in Manhattan and some of them are actually bigger than 1 bedrooms and definitely cheaper. Or, try looking in the East Village (around Alphabet City) or Chelsea.