As mentioned below, Richard II landed in South Wales on 24 July and, according to Adam of Usk, sent Thomas Despenser off to muster the men of Glamorgan. An interesting decision, because it suggests that Richard did not plan to advance via South Wales. (Otherwise why not just advance the whole army to Glamorgan and do the recruiting that way?) Presumably the intention was to do a Henry Tudor, that is, to move along the west coast of Wales and cut in towards Shrewsbury. This would (hopefully) allow for a junction with Salisbury and the men of Cheshire.
The problem was this involved hanging around - by 29 July Richard was no further on than Whitland Abbey, still west of Carmarthen! Here he met some of York's messengers. It took him two days more to get to Carmarthen, and there he got word of York's surrender. It's possible he also had word of the fall of Bristol. Despenser had returned by this time, with little or no reinforcement.
At this point Richard completely lost his bottle. He fled at midnight, disguised as a poor priest, taking with him only fifteen companions. These included his half-brother, Exeter, his half-nephew, Surrey, Thomas Despenser, and the bishops of Carlisle, Lincoln (Henry Beaufort!) and St David's. He apparently believed there was a plot to seize him. He objective was to join Salisbury with his portion of the army in the north.
Among those left behind (and probably very cross!) were Edward of York, Duke of Aumale and Thomas Percy, Earl of Worcester. These two were probably suspected of conspiracy, given their close blood ties to York and Northumberland respectively.
Worcester (Northumberland's brother) was the steward of the king's household. Weeping bitterly (if we are to believe Walsingham) he broke his staff of office and told the King's followers they were free to disperse. Then he and Edward (and probably quite a few others!) cut off across country to submit to Henry. What else were they to do?
Richard and his small band of brothers set off on a journey of about 200 miles across what was then very rough country indeed. Those of you who know Wales will be aware of the hills and estuaries in between Carmarthen and Conwy. Imagine that journey with no decent roads, no proper maps, and probably little local knowledge among the party. It took them a good 10 days, and when they got to Conwy it was to find that Salisbury had not been able to keep his men together!
At this point, Richard should have had an Edward IV moment. There were ships in the harbour and they could have sailed straight back to Ireland, where they had left 1500 men and most of the artillery in charge of the 16 year-old Edmund Holland, Surrey's brother. At worst they could have got from there to France and sought assistance. Instead, with absolutely no cards in his hand, Richard decided to negotiate. He sent Surrey and Exeter off to Chester, to parley with Henry.