Did Cleo and Beth have sex?

Probably not

While indeed we can see that Cleo is sleeping in Beth's bed in the hotel, I don't think that it means that they had sex. They indeed have returned to the hotel together and it seems that they've been drinking afterwards, but when the hotel staff member knocks on the door, we can see that Beth wakes up... in the bathtub, wearing still the same dress as the night before.

On top of that, we know that both Beth and Cleo prefer men - while the former has a bit clinical approach to sex, she never displayed a sexual interest in women and when we met Cleo, she admits living in a polygamous relationship with two guys.

So besides the fact that Cleo has slept in Beth's bed (without Beth sleeping next to her), there are no other proofs that would say that they had sex. Most likely, they got drunk, went to Beth's room, got drunk more and eventually passed out.

Of course, it is possible that after drinking too much, they indeed had sex without Beth fully undressing (she could have put he dress back afterwards too) and afterwards Beth decides to have a bath in her clothes. It just seems less likely.

Probably

did Cleo and Beth have sex?

It's open to interpretation, but my interpretation is that yes, Beth had sex with Cleo. At the very least, the viewer is intended to see it as a possibility, if not the only possibility.

In the opening sequence of the first episode, we see only a dark-haired head in the bed, and Beth hesitates and gives a brief glance in that direction in her rush to leave the room to get to the game. While the look is ambiguous, it certainly seems significant; she seems to be feeling some way or another about the person's presence.

In episode 6, the events of the night before are shown with the viewer keenly aware of what happens in the morning. Beth intends to have a quiet night in; the viewer knows the phone call is going to upset that. Cleo's appearance is small surprise; they hit it off at Benny's and Cleo told Beth to look her up in Paris. Cleo was flirtatious with Beth (although not blatantly so) in New York; we know Cleo is sexually unconventional. When Beth declines to join Cleo in the bar, the viewer knows she will; when she says she'll stop at one drink, the viewer knows she won't. The last thing we see is Cleo leading her to flirt with the strangers in the bar.

The next morning, throughout the reprise of the opening of the first episode, the question isn't "did she have sex with someone"; by the conventions of TV and movies, the glance at the sleeping form in the hotel bed the morning after a bender can't mean anything other than that she had sex with someone¹. The question is: did she have sex with Cleo or with a random guy from the hotel bar? Showing Cleo in the bed answers that question.

If they did, then does that make Beth bi?

Again, it's open to interpretation. My interpretation is that Beth is bisexual, though she may not embrace that identity and may not go on to sleep with other women. Throughout the series, Beth is shown rejecting social norms of all sorts. I don't see any reason she'd limit her choice of partners to one gender or the other. Beth's declared love for Townes, who is strongly coded as bisexual, also supports the interpretation.

¹ On the other hand, the show does subvert some visual media conventions in anticlimactic ways.

She wakes up in a bathtub away from the bed and with the clothes she had the night before, she looks towards the bed because she doesn't even know who it may be, I don't think she has had sex or is bisexual.