The question of whether Democrats "denied the legitimacy" of the elections of the Bush presidents and Donald Trump can be complex and should be addressed with nuance. Public opinion within a political party can be varied, and the term "Democrats" can refer to a wide range of people, from grassroots supporters to elected officials.
George H.W. Bush (1988)
In the 1988 presidential election, George H.W. Bush won against Michael Dukakis by a significant margin, and there wasn't a widespread movement among Democrats to challenge the legitimacy of his election.
George W. Bush (2000 & 2004)
The election of George W. Bush in 2000 was highly contested, especially due to the recount in Florida. The U.S. Supreme Court eventually halted the recount in a 5-4 decision in the case of Bush v. Gore, and George W. Bush was declared the winner. Some Democrats, including elected officials, expressed concern over the way the election was decided but did not uniformly claim it was illegitimate.
The 2004 election was less controversial, although there were questions raised about voting procedures in Ohio. However, these concerns did not lead to a widespread Democratic denial of George W. Bush's legitimacy as president.
Donald Trump (2016 & 2020)
Donald Trump's 2016 victory was met with shock and surprise, especially since many polls had predicted a Hillary Clinton win. While there were questions about Russian interference and its potential impact on the election, leading Democratic figures such as Hillary Clinton and Barack Obama acknowledged Trump's win and facilitated the transfer of power.
However, it should be noted that investigations into Russian interference were supported by many Democrats, and some individuals did question the legitimacy of Trump's presidency on those grounds. The 2020 election saw Trump himself contesting the results, claiming fraud without substantial evidence. Democrats widely accepted the 2020 outcome and saw Joe Biden as the legitimate winner.
In summary, while there have been Democratic individuals and factions that have questioned the circumstances surrounding these elections, it would be an oversimplification to say that Democrats as a whole "denied the legitimacy" of these Republican presidents.