as far as I'm concerned the game "Bump" is entirely based on luck, so you cannot really do anything to win, that pushing thing doesn't help much either. I also heard that you win easier if your tama is heavy, but I never saw any proof for that.
I personally really dislike this game, mainly because it's fully based on luck, takes up much time and still most of the times ends up in tears for me as well (I mean my tama loses too...), so I don't play with it too often. also this is the reason why I like V2s the least, luck-based games are not quite effective in making tamas happier, thus they are more difficult to take care for than a Plus, for example, where both the "Dance" and the "Jump" games are skill-based, luck doesn't have a role, so I enjoy them more, and if I am doing well it is easier to please my tamas via games.