The Welshman made the switch to the Bernabeu in a world-record move from Tottenham last September, and scored 15 times in 27 La Liga appearances.
Bale also contributed as Real collected the Copa del Rey and UEFA Champions League titles, scoring in both finals.
However, the 24-year-old is confident his best is yet to come, while also stating Real are eager to build on their successes last season.
"I'm really happy at Real Madrid and next year I'm sure I'll be better," Bale said while on a promotional visit to Jakarta.
"We want to retain the Champions League next season and become the first team to win two consecutively."
Bale is hoping to emulate his domestic success on the international stage, and though Wales failed to qualify for the 2014 FIFA World Cup he is hopeful of helping the team reach future major tournaments.
"I'm very proud to have been born in my country and I will fight to take Wales as high as possible and be a part of important tournaments in the future."
