Yep, surface tension is the key. With a bubble blown from a bubble-blower (which I guess is what initiated it) you have a slightly-higher pressure on the inside, counteracted by the surface tension. (The surface tension on the outside also pulls inwards.) Hence the balance needed to make a bubble.
(Actually, this is a vague stab at the physics of it, so maybe sombody will prove me wrong…)
That’s different - it’s a bubble within a liquid, rather than one on the surface. One in the liquid can reach the surface and burst, or it can reach the surface and become a bubble as has been described already.