This would be modern, rather than early modern, but D.A. Kinsley's "Swordsmen of the British Empire" has a 30 page chapter comprised of contemporary accounts of Bayonet vs Sword combat in Indian and other colonial wars. The format of this book is just the first hand anecdotes rather than analysis, but I'll do my best to summarize.

Bayonets were generally found inferior to swords in a swirling melee or chaotic assault. The swordsman was either able to parry (or block with shields and bucklers) and get inside the bayonet, or even if stabbed, fatally or otherwise was able to close with his opponent and deliver an equally fatal counter attack. There are dozens of firsthand accounts of Afgans, Sikhs, and Baluchi swordsman doing just that after receiving bayonet wounds. Despite it's general inferiority, Bayonets were thought to have the advantage when troops fought in very close order or charged in a close packed mass. These accounts are by both officers and enlisted men, but of course are almost entirely from the British point of view rather than from their colonized adversaries. As may perhaps be expected, there is a great deal of complaining about the quality of arms (both bayonets and swords, but especially the sword-bayonet) given to British soldiers by the British government with Indian Tulwars and other swords (as well as Zulu Assegai's and other weapons) given lavish praise in contrast.

However, all in all, I don't find the accounts totally convincing that the bayonet was always inferior to the sword. Perhaps the most we can say from this work is that men equipped with Bayonets by no means felt themselves better equipped than their sword wielding foes!