Is there a process to follow when creating Undead versions of monsters? I would like to create some Undead Bugbears but I'm unsure what needs to be done.

Do I just mashup Bugbear stats with Skeleton stats?

Thanks!

There are no special rules for any creature type. Many creatures have traits in common but even in those cases the details can vary.

You can use the skeleton stat block for any humanoid race; the Animate Dead spell doesn't care what race the corpses come from. Alternatively, DMG chapter 9 has a list of modifications you can apply to NPC stat blocks to account for their race, and skeletons are on the list.

When creating a new stat blocks from scratch, it's usually easiest to pick a similar creature as a starting point. The DMG has additional guidelines.

Quote from InquisitiveCoder >>

There are no special rules for any creature type. Many creatures have traits in common but even in those cases the details can vary.

You can use the skeleton stat block for any humanoid race; the Animate Dead spell doesn't care what race the corpses come from. Alternatively, DMG chapter 9 has a list of modifications you can apply to NPC stat blocks to account for their race, and skeletons are on the list.

When creating a new stat blocks from scratch, it's usually easiest to pick a similar creature as a starting point. The DMG has additional guidelines.

 Thanks for the feedback! :-)

I'd just take the time to look at the statblocks of various undead. See what makes them feel mechanically undead. Incorporate that element into the bugbear block. in 5e its mostly just fluff on how you describe monsters while the stats remain mostly the same.

A yellow furred bugbear, dressed in leather armor and studded shoulder pads, charges at you flanked by his two rats. Mace swinging up in the air ready to come crashing down...
vs
A bugbear with patches of his fur gone. Underneath is sickly white skin. Under his leather armor you can see parts of his skin gone showing fragments of bone. Eyes white as the moon above an unhinged jaw. It shambles toward you dragging the mace across the floor behind it. Flanked by two diseased looking rats.

Quote from Giblix >>

I'd just take the time to look at the statblocks of various undead. See what makes them feel mechanically undead. Incorporate that element into the bugbear block. in 5e its mostly just fluff on how you describe monsters while the stats remain mostly the same.

A yellow furred bugbear, dressed in leather armor and studded shoulder pads, charges at you flanked by his two rats. Mace swinging up in the air ready to come crashing down...
vs
A bugbear with patches of his fur gone. Underneath is sickly white skin. Under his leather armor you can see parts of his skin gone showing fragments of bone. Eyes white as the moon above an unhinged jaw. It shambles toward you dragging the mace across the floor behind it. Flanked by two diseased looking rats.

 Ooooh I like that... Admittedly that's a part of my DM'ing I'm working on: at the table descriptions.

I'll have to jot down some notes along those lines. And thanks for the suggestion of keeping the stats nearly the same for the bugbear.