Real kicked off the Julen Lopetegui era with a 2-0 win.
Bale declared: "I'm feeling good and, although I scored, the most important thing was that we got the win and are continuing to improve as a team.
"We're really looking forward to the season ahead. Our target, just like every year, is to win all of the competitions we're involved in and we'll be giving our all to do just that. The new signings have adjusted really quickly.
"We've given them a good welcome and I hope that they're all available in the near future."