There are two concerns with using your host’s linens. One is not to leave linens with the stains of the discharges that can result from intercourse. The other is to preserve modesty by not having the stains indicate that relations took place. Halacha does not address this question specifically, so it comes under the general category of “derech eretz” (fitting or polite behavior), which is also incumbent on us.
For purposes of modesty, it is sufficient to bring a towel or cloth to place over the sheet during relations. As far as not leaving stained linens for your friend to change – if you know that your friend does not expect you to bring your own linens, or you know that you will strip them in the morning, then it would not be required.
At a hotel, you are paying for the service of using their linen, which they will automatically launder. However, there is another reason to consider bringing your own linens – the fact that many hotels supply white sheets and white towels. If you were to find stains on the white sheets, you might become niddah, according to the laws of stains. This may be an unlikely possibility, but the issue could be avoided altogether by bringing colored towels to keep under you, and to clean yourselves with after relations.
Please feel free to be in touch with further questions.
This response was updated on 10 July, 2022.