a higher bonding is achieved mainly by "training" your tamagotchis when they call for it (for the v5, the possible training times are 10am, 12pm, 2pm, 4pm and 6pm). when they call for training, you have to choose the sixth icon which is otherwise not clickable!
other ways:
- the only games that can raise bonding are the games played with the tamagotchi parents which can only be played from second generation onwards.
- there also exist items that, when used, raise bonding. just google them. :mimitchi: