Royal Marines of the time period the Bolitho series covers - the early 19th century, roughly - would have been using a specific kind of service musket developed specifically for use on ships, the Sea Service Pattern musket. The Sea Service Pattern had a slightly shorter barrel than the land service muskets in use in the army, which by 1802 were the India Pattern service musket, which itself was a slightly simpler, slightly shorter version of the second pattern Land Service musket, which was a shorter version of the Long Land Pattern, etc.

A lot of details among these weapons are different, but in important features, the lock and the bore diameter, were pretty consistent. The biggest differences tended toward making the musket shorter and lighter and less expensive to produce. The number of ramrod pipes tended downward, and flourishes like a elegantly curved lockplate and escutcheon were replaced more and more with simpler elements, or removed entirely.

But to get to your question, the bayonets were more or less exactly the same in all of the standard service muskets used by the British military. It was a socket bayonet, meaning that the blade - a triangular spike with no sharp edges - was mounted on a cylindrical mount that slid over the barrel and locked in with a simple dogleg socket, which would keep the bayonet fixed even if the musket was jostled around a bit. This mount allowed the barrel to remain open, meaning that a soldier or marine could both reload and fire with the bayonet attached. Since reloading meant interacting directly with the barrel and using a ramrod, the bayonet mount was offset by an inch and a half or so, meaning that a soldier wouldn't risk hitting their hand on the point while using the ramrod. The bayonet's offset and pattern of socket would also mount the bayonet to right side of the barrel (the same side as the lock), which facilitated the British reloading practice.

It should be pointed out that Bolitho often specifies the quarterdeck marines with fixed bayonets; other marines, such as those in the tops or working in gun crews, would not necessarily need a fixed bayonet. The quarterdeck marines were a sort of bodyguard for the quarterdeck officers, and their main job was protecting those officers, not necessarily engaging in fire at the enemy ship.

So to make a long story short, the bayonet wouldn't interfere with loading the musket, though it might make it slightly more awkward.

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Lots of details about the particular pattern of army muskets can be found in Anthony Darling's Red Coat and Brown Bess