I would really appreciate it if you would answer my question clearly and concisely. Is there an Islamic basis to checking bed sheets for blood on one's wedding night to see if a wife is a virgin? What does Islam say about this? Is Islam in favour of this or does it see it as a bad thing?
I am anticipating your speedy reply.

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

The custom you are asking about is not Islamic and does not have any relation to Islam; rather Islamic Shariah hates and disapproves of it. The practice indicates serious ignorance of Shariah and shamelessness in society. Imam Muslim narrated in Sahih Muslim that the Prophet (Sallallahu Alaihi wa Sallam) said: "The most wicked among the people in the sight of Allah on The Day of Judgment is the man who goes to his wife and she comes to him, and then he divulges her secret." Muslim

Imam al-Nawawi wrote explaining the Hadith: "The Hadith proves that disclosing the sexual actions, words, etc that occurs between a husband and his wife is strictly forbidden."

What act can be more indecent than showing the people the blood of removal of hymen? No doubt the prohibition mentioned in the above Hadith covers this act too. Also, such a practice is a way of spying and trying to know the secrets of a Muslim which is forbidden. It may lead to a suspicion about a Muslim woman since bleeding is not a criterion for proving virginity since an illness or physical exertion, etc. can be a cause for the removal of her hymen.

Allah knows best.