Why doesn t the BDS movement actively try to encourage peace and build bridges between Palestinians and Israelis ?

You are confused. It is the other way around. Zionists do not want real peace, they want complete subjugation of Palestinians under their boots, and expansion of more illegal settlements on Palestinian lands. God forbid anyone from speaking against Israeli human rights violations. People who do, will be bombarded with antisemitic false allegations.
Since their arrival, the Zionist settlers exploited Palestinian hospitality and worked towards the aim of establishing an ethnocratic settler state at their expense. They banned Arab workers, established a Jewish only trade union, and censored those buying Arab products or those cooperating with them in any manner. As Menachem Usishkin, chairman of the Jewish National Fund said, they wanted to be the “landlords of this land”. Even before any physical Zionist settlement, Herzl wrote about ways to get rid of the population already living there.
I see the other replies by Zionists rather ridiculous, and devoid of reality through targeting a non-violent movement against Israeli oppression like BDS. The same ridiculous arguments that were used by South African apartheid supporters in the past. History does in fact repeats itself.
You hear something, you see it happening…. You have to believe it. Israel never wanted peace. The only peace it wants, is another piece of Palestine.