How does Shakespeare present the court and courtiers in Richard II?

In the opening scene of Richard II, Shakespeare launches his audience into the middle of a charged argument between two prominent nobles: Henry Bolingbroke and Thomas Mowbray. The quarrel is arbitrated by the king of England, Richard II, who immediately asks John of Gaunt, “Tell me, moreover, hast thou sounded him, If he appeal the duke on ancient malice . . . ?” The fact that Richard II jumps to the conclusion that this debate could be the result of some petty “ancient malice” signals to the audience that Richard II’s court is a tumultuous place, full of partisanship, laden with gossip, and primed for violence.
While there are several characters we could analyze in answer to your question, I believe some of the most interesting are Richard II’s loyal supporters Bushy, Greene, and Bagot. Greene is particularly influential in persuading Richard II to focus his attention on the war in Ireland, which is viewed with distaste by the wiser characters of the play. The three sycophants continually flatter Richard II throughout the opening acts of the play and are the object of much disdain from other characters. The Duke of York, Richard II’s uncle, complains of his nephew “all in vain comes counsel to his ear” because “it is stopp’d with other flattering sounds.” John of Gaunt aches to provide Richard II with “wholesome counsel” rather than the drivel he receives from the “thousand flatterers that wit within [his] crown." Henry Bolingbroke refers to Bushy, Bagot, and Green as “parasites” and bitterly calls them the “caterpillars of the commonwealth.” Clearly, these courtiers are presented in a negative light by Shakespeare because they cloud Richard II’s judgment and understanding of the important issues facing his kingdom. Clearly, these prominent courtiers are presented as a negative influence on Richard II.
However, Bushy, Greene and Bagot’s influence in the early scenes of the play is also an indictment of Richard II’s immaturity and irresponsibility. Richard II willingly chose to surround himself with yes-men rather than accepting the advice proffered by his older and wiser advisors such as Gaunt or York. For those seeking to depose Richard II from his throne, the king’s misplaced trust in the “caterpillars of the commonwealth” is a prime example of why he is unfit to rule England.
Ultimately, Henry Bolingbroke exacts justice on Bushy and Greene by executing them in act 2, while Bagot betrays Richard II and flees to Ireland. The fact that most major characters treat Bushy, Bagot, and Greene with disdain and that all three meet dishonorable ends shows that Shakespeare intended that they be reviled and disliked by the audience. I hope this helps!