The plot of 1583 was a real plot, called the Throckmorton Plot, though it probably did not play out exactly as in this story. Sir Francis Throckmorton was identified as the main conspirator, and arrested after evidence was found at his house. He confessed under torture. Throckmorton said he acted as a Spanish agent, and that the plan was to assassinate Elizabeth and put Mary on the throne. This was to be accompanied by a simultaneous invasion of England by Henry I, Duke of Guise, financed by King Philip of Spain. Meanwhile, the Catholics of England would be incited into rebellion.
Throckmorton was executed for high treason, and Mary placed under very strict watch in Chartley Hall in Staffordshire. Mendoza, the Spanish ambassador, was expelled from England for his part in the plot. In 1584 the Bond of Association was created and signed. It obliged all signatories to execute any person who tried to assassinate the Queen or to take her place. It also forced them to hunt down the killer if Elizabeth should ever be successfully assassinated. Mary Stuart was one of the signatories.
It was not until the Babington Plot in 1586 that evidence of Mary’s involvement in trying to depose Elizabeth was found. Though Mary denied her role in the plot, her correspondence condemned her, and she was beheaded for treason in 1587.
Read this article for more about the real events behind the book, and Bruno's own possible role as a spy.