The former champions are the only absentees from the five days of running at the Circuit de Catalunya that started on Monday.
Media reports had speculated about there being a problem with the car passing the FIA crash tests required to participate, but Vowles told reporters there were no longer any hurdles.
"I'm pleased to say that we've passed all necessary tests and we're ready to run in Bahrain, and we'll carry out a promotional filming day ahead of it," he said in a video call.
"We're also carrying out a VTT (virtual test track) as a physical car testing rig... we've been running that pretty much in tandem to Barcelona."
Vowles said the decision to miss the Barcelona week stemmed from the team's "determination to push the limits of performance under the new regulations."
He said Williams could have taken part, but only by compromising on spare parts, updates and preparations for the Bahrain tests and the start of the season in Australia.
"The car this year that we've built...is about three times more complicated than anything we have put through our business beforehand," he said.
"It means the amount of load going through our system is about three times what it used to be, and we started falling a little bit behind and late on parts."
Vowles referred to certain unspecified tests as "a blip in the grand scheme of things" that pushed the team beyond the limit of what could be achieved in the time available, particularly in the supply of components.
"We're in this halfway house where we're using systems, and where they're not quite for purpose, we're falling back to old techniques and human glue, and that's what's causing the problem with that," he said.
Vowles brushed aside as "murmurings in the media" suggestions that the car was significantly overweight and said drivers Carlos Sainz and Alex Albon stood "shoulder to shoulder" with him.
Williams finished fifth in the team standings last season, their best since 2017. The 2026 campaign begins with the Australian Grand Prix in Melbourne on March 8th.