York's 'agreement' with Henry, however reluctantly it may have been made (or not), had one important effect. York was the legitimate Keeper of England and his adherence to Henry lent some shred of legality to the cause.
Together they moved on to Bristol, where the freedom-loving Henry announced that anyone who came out of the city in peace would be spared, but anyone who stayed within the walls and resisted would be killed. This led to a pretty prompt surrender of the city, with some citizens even climbing over the walls in their haste to survive. The castle followed suit. Within, among others, were the Earl of Wiltshire (William Scrope), Sir John Bushey and Sir Henry Green, all prominent councillors of King Richard. Bushey had acted as Speaker of the Commons.
The next day, these three were summarily executed; at best they might have had a drum-head trial before Northumberland and Westmorland, acting as constable and marshal. Either way it was unquestionably an illegal act, and one that was intended to strike terror into Henry's opponents.
Reams of print have been used up condemning Richard III for executing Rivers, Grey and Vaughan. However, Richard was at least established as Protector when he gave the order and had the pretext that they'd been plotting against him in that role. Strangely, it is rare to find a single word of criticism for Henry's outright murder of these three men. Lancastrian kings, it appears, can do no wrong.
Sir John Russell, the King's Master of Horse, would also have been executed, except that he lost his mind. Temporarily, it seems, but effectively, because he was spared. Russell had been briefly married to Thomas Despenser's very young niece, Margaret Hastings, but she must have died within a year or so, probably through the hazards of childbirth, as by 1399 he was remarried to a wealthy widow. He was also a personal enemy of the Earl of Warwick, whose retainer he had been before defecting to Richard. By the way, if you want to visit Sir John he's got a nice brass in Strensham Church, which is now in care of the Churches Conservation Trust.