Bale salvaged a victory for Wales on Friday, with his late goal securing a 2-1 home win over Azerbaijan.
The win lifted Wales on to six points from their four games in Group E, and though they sit in fourth, they are only three points behind joint-leaders Croatia and Hungary.
Slovakia are level with Wales as it stands, and the sides will face off in what could be a crucial qualifier on October 10.
Though Bale acknowledged the squad are still working on adapting to Giggs' desired style of play, he is in no doubt Wales - semi-finalists at Euro 2016 - can qualify for next year's tournament.
"Yeah definitely, I wouldn't be here otherwise, I would not be wasting my time," Bale told a news conference ahead of Monday's friendly against Belarus.
"I love playing for my country, I love trying to qualify for major tournaments and having that taste of it at Euro 2016 gives you that hunger to do it again and to experience what we did.
"We all still fully believe we can and we hope the public still believes and give us all the support we need because they're the 12th man.
"I think we're still working on things and there's things we're improving on. We're working on [Giggs'] style of play, what he wants us to do and sometimes it does take a bit of time.
"I think that's why it's good now to have a friendly. A match situation is always more intense and more difficult to do things than in training.
"We still want to keep that winning mentality and get that momentum building and by winning games that's what you do."
Bale's header against Azerbaijan took the 30-year-old four clear of Ian Rush as the leading scorer in Wales' history with 32, and the Real Madrid forward acknowledged he has a target of international goals in mind.
"I've got a little target in my head but it's just one of those personal goals," Wales' captain added.
"If I achieve it, great, but if I don't then it's okay. It's something I'd like to do but the most important thing is to win games for my country and to give fans something to cheer about."