Shalom Israel,

It's great to hear from you. What a wonderful question! Since the Bechoros played the role of the Kohanim at that time (112b), my first thought would be that unless the owner himself brought the Korban, the Bechor who offers the Korban should also receive the hide. But I have not yet seen this discussed explicitly, so I would like to continue researching it, and will be happy to let you know if I find something more definitive.

After I wrote the above paragraph, I found a more explicit source. The Yerushalmi (Megilah 1:12) states: "Rebbi Zeira in the name of Rebbi Lazar says that indeed the owner receives the hide from an Olah offered on a Bamah Ketanah." (Yeyasher Kocho to Rabbi Avraham Yaakov Sherer for pointing this out to me.)

Bi'Verachah,

Yishai Rasowsky