In the source novel (The Book of Strange New Things by Michael Faber), the outward journey takes around thirty days. It's not clear whether this is the same in the TV movie (given how many other changes that were made), but there's really no good reason to assume that this was altered.
He closed the book. His hands were trembling. He knew that there was quite a decent chance that he would die in the next thirty days, or that, even if he survived the journey, he would never return.
The cannula was in his vein; the IV drip was activated; the
translucent substance moved into him. He thought he might vomit from
the sheer ghastliness of it. They ought to have given him a sedative
or something. He wondered if his three fellow travelers were braver
than him. They were nestled in identical cribs, elsewhere in the
building, but he couldn’t see them. He would meet them in a month from
now, when he woke up.
Note that in the original book, travel between Earth and Oasis was sufficiently commonplace that several of the characters had made multiple trips to and from the planet in the previous years whereas in the film it's more of a "one way trip, and you might be able to return to Earth in a few decades time" deal.