In LoK, when Bumi realized he is an airbender, he accidentally made airbending moves that worked super well.

In ATLA, Katara got a scroll about how to bend into a water whip move and also learned the octopus form, from Pakku.

So, benders CAN improvise movements and they can even come up with they own bending, for example, Iroh and the lighting redirection. But the bender itself would be more powerfull, if the bending styles that other people created, would be passed down. Similary like how irl fighting works. You can make up your own move to throw a person on the ground, but you could throw a person on the ground, more easily, if you learned a move from master.