The most unlikely long-distance friendship is blossoming between the "I Don't Care" singer and the Cleveland Indians ace ... with the Biebs getting his own "Not Shane Bieber" Tribe jersey!!!

Of course ... Shane has worn "Not Justin" on his back for the past 2 MLB Players' Weekends, when the athletes get to wear whatever name they want on their jerseys.

JB is getting in on the fun now ... rockin' his very own Tribe jersey while joyridin' on his motorcycle in Beverly Hills on Tuesday.

The 2 first linked up online on August 4 after Topps accidentally called Shane "Justin" on his baseball card -- and Justin responded on Twitter, saying, "I feel like we have a special connection."

TMZ Sports spoke with Shane in NYC earlier this month and he told us that the interaction was a life milestone reached.