Getting the different forms of Burmy is less about catching one in the form you want, but more about where it last participated in battle. The form Burmy is caught in is not permanent, and will change when you use it in battle in certain locations. This allows you to catch any Burmy, regardless of where it is, and choose which form you'd like it to be in when it evolves into Wormadam and its cloak becomes permanent (assuming the Burmy in question is female).
If Burmy last participated in a a battle that took place in grassy or watery areas, it will appear in Plant Cloak. If its last battle was in a sandy or rocky area, it will appear in its Sandy Cloak. If it last fought in a building or built-up area, it will change to its Trash Cloak.
As for other Pokemon with multiple forms, there are far too many to list in one answer, so instead I'll recommend that you read this Bubapedia article that lists them all and explains how they're each obtained.