You should have brought your a8 rook into play by playing 27...Rg8. You should not try to catch the bishop and/or rook. You had a huge material advantage and two passed pawns. As long as you do not have an unprotected piece you would not have been in danger in this game. Just push the pawns and white would eventually lose a bishop or a rook to stop them.
How could I have played this endgame better?
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Thank you!
Yeah we 700 rateds are real geniuses 😎
Only when they are in royal blood lines 
I just played this game where I went into the endgame around move 20 with a sizeable advantage, but I struggled to finish him off, and even blundered a couple of pawns. I was unsure how to get rid of his bishop and rook. I got there in the end, but I could easily have blundered a piece somewhere if I wasn't careful. What is the best strategy in a situation like this to get rid of the rook/bishop?