The writers and director claim that they didn't know about the TARDIS. To decide whether that is plausible or not, it is worth considering the differences between the two:
The Doctor's TARDIS is not a public phone box - it is a British Police box. The time machine in Bill & Ted is based on a regular public phone box.
The telephone on a Police box is ...
Co-writer Chris Matheson claims that neither he, nor co-writer Ed Solomon nor the film's director Stephen Herek (who suggested the phone box) knew anything about Doctor Who.
“Rufus was originally their friend,” reveals Matheson of Bill and
Ted’s time-travel mentor, played cooly by comedian George Carlin. “He
was a 27-year-old high school junior and ...