There a few rather informal alternatives: à plus, à la prochaine, à la revoyure, tchao, tchuss… The first two are closer to à bientôt (i.e. suggest that you are likely to see the person again soon), whereas the other are closer to au revoir (which just means “bye” despite what a literal translation might suggest). If you have a specific plan it’s also possible to end a conversation with something like à lundi.

Finally, bonne journée (ou bonne soirée, bon après-midi, bonne continuation, bonne route, etc.) is also common, often together with au revoir or à bientôt (and not necessarily as a replacement).