I was riding my bicycle alongside all the cars that were backed up in traffic.
I rode my bicycle beside the big line of cars that were stuck in traffic.
どちらも「渋滞した車の列の横を自転車で走った。」という意味で使える言い方です。
「自転車に乗る」は ride one's bicycle
「〜の横」は alongside や beside を使えます
cars that were backed up in traffic 「渋滞で滞っている車」
big line of cars that were stuck in traffic 「渋滞にはまった車の長蛇の列」
ご参考になれば幸いです！
日本 
