Bale won his third Champions League winner's medal in four seasons as Real swept aside Juventus 4-1 in his home city of Cardiff on Saturday night.
"It has been a great year", Zidane said after the final whistle.
Real Madrid players celebrate at the end of the Champions League soccer final between Juventus and Real Madrid at the Millennium Stadium in Cardiff, Wales, Saturday, June 3, 2017.
"My family is happy and I am happy, so yes we will continue what we are doing".
Real's victory saw them become European champions for a record 12th time as Zinedine Zidane's side became the first club to retain the trophy in the Champions League era.
The Portugal forward seems more focussed on poaching goals in the box rather than making headway out wide and his efforts were pivotal in Real Madrid's excellent 2016-17 season, during which Los Blancos won their first La Liga title since 2012 and a second consecutive Champions League. Then came the Club World Cup with Real Madrid and the end of a five-year Spanish title drought before new highs were reached in the Champions League.
"We won a double that will be in history".
"This club is really in my heart and we are going to enjoy this".More news: Larson, Truex take top 2 spots in Michigan qualifying
"I think the project is well laid out", Madrid president Florentino Perez said. When the stars didn't play, the youngsters did and they did well.
Gonzalo Higuain worked Keylor Navas twice, while Miralem Pjanic's snappy half-volley forced the Madrid goalkeeper into a smart one-handed save.
"Cristiano Ronaldo gave his point of view of yesterday's final:" It has been a very even game.
Bonucci's flighted pass from deep was volleyed into the box by Alex Sandro and Higuain chested the ball down before teeing it up for Mandzukic.
The Brazilian midfielder unleashed a shot from 25 yards that flicked off the heels of Madrid old boy Sami Khedira before spinning past the helpless Buffon.
Asensio added: "Since the beginning of the season I knew I wanted to stay here, I wanted to gain minutes to play these kind of games and it's been an incredible season".
Luka Modric sped to the byline on the right and crossed as Ronaldo darted ahead of Bonucci at the near post to guide a shot past Buffon.
Local boy Bale made a late cameo appearance, coming on for Karim Benzema in the 77th minute with the job done.