Bale has been pivotal for Wales, scoring seven goals during the European qualifiers, and led the country to their first international tournament finals since 1958.
The 26-year-old suffered from cramp during Real's victory but he reassured Wales he would be fit when the 24-team tournament kicks off on June 10.
"My confidence is high especially after winning so I am looking forward to going to the Euros," Bale told British media.
"There's four or five days between each game so it's normal. We play every two or three days with our club teams
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"I'm confident everyone will be fit enough and firing and hopefully we can... You never know... Two trophies in a matter of months!"
Wales face Russia, England and Slovakia, their first opponents, in Group B of the European Championship in France.
(Reporting by Shravanth Vijayakumar in Bengaluru; Editing by John O'Brien)
