Super Princess Peach
Blue Lava Bubbles first appear in Super Princess Peach as enemies appearing in Bowser's Villa. They hop out of blue lava and will home in on you when they see you. They can only be defeated by luring them into a fire cup which can also be used to open the path forward.
Super Mario Galaxy series
Blue Lava Bubbles appear as the blue, possibly colder, counterparts to normal Lava Bubbles. They are commonly seen around King Kaliente, who is a boss in Good Egg Galaxy and is one of Bowser Jr.'s commanders. They also appear in Boss Blitz Galaxy (Galaxy 2) and Melty Molten Galaxy (Galaxy). The only way to defeat them is by shooting Star Bits.
Super Mario 3D World
In the Wii U game, Super Mario 3D World, Blue Lava Bubbles are more common than they were in the Galaxy series. There are now stages dedicated to blue lava and the Blue Lava Bubbles, one example being Castle-4: Boiling Blue Bully Belt. Blue Lava Bubbles can no longer be defeated and look slightly different from their other appearances.