"To have the Champions League final in my home town is an even bigger motivation," he said.
The Wales international helped Real beat Atletico Madrid on penalties to march to their 11th European title and his second with the club in the 2015-16 campaign before playing for his country at Euro 2016.
"Two in three years is an amazing achievement," he said. "Now we want to look to the next one."
Injuries limited Bale to 30 appearances in all competitions for Real last season but the former Tottenham star still scored 19 goals and provided 10 assists.
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Bale is on a 10-man shortlist for UEFA's Best Player in Europe award. The winner will be announced on Thursday in Monaco during the 2016-17 Champions League draw.
"It was an incredible season, especially topping it off by winning the Champions League and then going on to the Euro and doing an amazing job with Wales," he said. "They were two great moments in my career, in my life."
Wales made it to the semi-finals before falling to eventual champions Portugal in July.
Bale has had a strong start in his fourth season with Real, scoring twice in his team's 3-0 win at Real Sociedad in their La Liga opener on Sunday.
(Reporting by Adriana Garcia; Editing by Raissa Kasolowsky)
