Ok, the best way to win BUMP is to get you tamagotchi overweight.
Toddler- Get it to 25 LB
Teen- Get it to 30 LB
Adult- Get it to 55 LB or more.
Next you must push B fast when it says "PUSH". Only I keep pressing B so I'll have a better chance of winning. As soon as you see your tamagotchi's apponint, start pressing B as fast as you. When they start to BUMP each other, you can stop pressing B. If your tamagotchi wins, it will move to round 2. I believe there are 8-10 rounds in bump.
Hope I helped!
*~Tamagotchi~*