Yes, bismuth is safe in your older Browning, as is ITM (tungsten matrix) and NICE shot. Another one not mentioned is ITX shot from Ballistic products; however, to the best of my knowledge, it is currently only available as a reloading component.
Two other loadings that are available in loaded shotshells are "Tundra", by Fiocchi and Hevishot classic doubles, both of which are safe in older, fixed choked guns.
As stated previously, none of these alternatives are as cheap as steel shot.
Good luck and good hunting...............