The Glorified Allah commands:
“O you who believe! When you rise to perform prayer, wash your faces and your forearms to the elbows and wipe over your heads and your feet to the ankles. And if you are in a state of janabah, then purify yourselves. But if you are ill or on a journey or one of you comes from the place of relieving himself or you have contacted women and do not find water, then seek clean earth and wipe over your faces and hands with it. Allah does not desire to put on you any difficulty, but He wishes to purify you that you may be grateful.” (Al-Ma’ida/ The Feast 5:6)
As we can understand from the underlined verses, in order to take dry ablution, there must be lack of water or even if there is water, it should be infeasible to use because of disease or other extraordinary reasons. Therefore, dry ablution should not be performed if you have opportunity to use water, even though you are travelling. It is also valid for visits. ‘Being embarrassed’ is not a condition of the verses mentioned above. Therefore, you have to take ghusl in such cases.
You should not put yourself into these kinds of unnecessary troubles. The parents, children, bride, husband’s sister and wife’s brother used to live together in the same house 20-25 years ago. The bathrooms were common, and, moreover, it was too hard to find the hot water, but in spite of everything, life went on, and we have reached today. This sort of things would not be a cause to feel embarrassement. If you need to take ghusl for whatever reason it might be, you have to do it. If there is an opportunity to take ghusl, dry ablution (tayammum) or wudu would not be accepted.
If the water flows over your skin while you are wiping your body with a wet rag, that could be accepted as taking a bath, otherwise it would not be ghusl.