No one ever questioned why Charlie always sat on Vinnie's bike whenever the trio rode and Charlie didn't have her own bike. In reality, no one needed to. There was space on Throttle's bike if Charlie ever needed a ride, but Throttle knew better than to mention it. Modo even had a small spot on the back of his bike, but Modo didn't bother either.
Vinnie had a very horrible way of accepting and receiving affection, even if he was plain as day to read. Charlie was one of the smartest humans the mice had ever seen and could read Vinnie like a book and had done so more ways than one. Throttle and Modo figured the reason why Charlie didn't do anything with or to Vinnie was because that she didn't want to make Vinnie higher than thou more than he already was.
Throttle and Modo had seen more than enough to convince them that Charlie was true and not just playing around. The number of times she'd hugged Vinnie, the kisses she blew his way, the times she was close to Vinnie...all plain as day even if Vinnie often misread most of them. Throttle and Modo knew that Vinnie was young and the only other interest he ever had was in Harley, but the pair wisely never dwelled on that and the what-ifs. They also ignored the fact that Charlie was quite like Harley in some aspects.
Perhaps the reason why Vinnie and Charlie never showed each other more affection in public was due to the embarrassment that Throttle and Modo would definitely dish back to all that Vinnie gave to Throttle on occasion and even Modo when he had shown some interest in the bird bounty hunter a little while back. The pair had seen a few pieces here and there and had razzed Vinnie when they knew it was allowed. Throttle and Modo didn't want to pick on Vinnie too much because he would close off in response to protect his manly exterior and the pair wouldn't do that to Charlie.
Throttle and Modo knew that the two had issues not only being different species, but being from different planets, and Vinnie's mind was crowded with the issues of invincibility that invaded all young people's minds. The two hoped that after a while of Charlie being there and showing Vinnie that the mouse would open his eyes and eventually act accordingly.
Throttle and Modo waited for the day for that one time when Charlie wrapped her arms around Vinnie's waist when on his bike that it would click and the biker would know. Perhaps Vinnie already knew? Throttle and Modo hoped so because they really liked Charlie and wanted the best for her. Despite being a danger maniac, Vinnie was a good mouse and the pair worked. That was one reason why Throttle or Modo never offered Charlie a ride on their bike. They let Charlie do her silent expressions to Vinnie and observed the pair.