There is no real way of telling the age of a betta fish, unless:
1) You bought the fish from a breeder in which took records of the birth.
2) The betta fish is still in its fry stages (Which would be unlikely because then you probably wouldn't have it anyhow)
I'm assuming that you bought a pet-store bought betta. These can be in any age bracket, so its as unpredictable as possibly being 7 months old to a year and a half. Sorry I can't be more helpful =( Just the unfortuent fact I believe.