I agreed with
kno4te in that a bowfin (assuming you get it very small) can live comfortably in a 125 for 1-2 years.
As for how big they get, bowfin will reach 20-28 inches when fully grown in the wild (the world record is 34 inches), so in an aquarium it is safe to assume a bowfin will reach 18-24 inches . I think a 6'x3'x2' would be a good bet to keep a bowfin for life (unless you get an exceptionally large one. Here is a care guide on bowfin written by another member.