Commentary for Kiddushin 129:23

The Talmud now assumes that in this mishnah there were witnesses, but only witnesses that they were secluded, not that they had intercourse, which would constitute betrothal. Bet Shammai says that this is not sufficient to create an assumption of sex and betrothal and therefore she does not require a divorce. Bet Hillel says it is sufficient.
However, they both agree that if the couple had not previously had intercourse because they were never married, then she does not require a get. In such a circumstance, we cannot assume that they had sex at the inn.