The Welshman moved to the Santiago Bernabeu from Tottenham Hotspur in a world-record £85m deal last summer and has since scored 20 goals in 35 appearances, including a late winner in the Copa del Rey final against Barcelona.
His form has helped Madrid stay in the Primera Division title race, and a 5-0 aggregate victory over Bayern Munich in a European semi-final means that Carlo Ancelotti's side are still in with a chance of the treble.
At the Allianz Arena, Bale feels that Sergio Ramos's early headed goal was a pivotal moment as it allowed Real to play on the break, which they did to great effect, thrashing the Bavarians 4-0 in Germany.
"It's an amazing feeling," he told Sky Sports News. "At the start of the season it's hard to imagine. We set out to try and win every competition we're in and we're in a great position now.
"We always have belief in ourselves. To get an early goal was very important for us to give us confidence. They were going to come at us then and we could exploit the counter-attack.
"It was a perfect game-plan for us and thankfully we got the win. I think we played a good game in both legs and we're happy to be in the final now. We're just focused on each and every game as it comes. We don't get carried away with ourselves too easily."
Madrid are six points behind leaders Atletico Madrid in the Spanish table, but do have a game in hand over their city rivals.