Can a soap bubble bounce off a laser?

The clip you link is not from a controlled experiment. The simplest explanation is that the laser beam heats the air and the convection pushes the bubbles.

I would think that if the laser hits a bubble wall directly the heat would make the wall collapse, but it needs a controlled experiment to really study the interaction of "green laser beam" with soap bubbles.

I can rule out momentum transfer from the laser. Even though radiation pressure is a thing, it is far too low to be noticeable. Let's do the math: Radiation pressure p=I/c (c speed of light) is determined by the intensity I of the laser beam. Since pressure in general is p=F/A (F Force and A Area), you get F=I*A/c for the force that results from the laserbeam to an object (A beeing the area of the beam, not the object). Since I*A is simply the power P of a laser you get F=P/c, assuming the laser beam lies completely within the object's surface area. Now let's compare with the weight (not mass) of an object. The weight of an object is m*g (m mass, g gravitational accelaration on earth). So setting m*g=P/c, you get m=P/(c*g) for the mass of a weight that would have the same force on the object as the laser through radiation pressure. Assuming the laser in the video has a power of 1W (which it definetly does not have, judging by the overall brightness and the sheer carelessness of the dude waving it around the lab), you get a mass of 0.3 microgramm. For comparison: A 10cm long human hair approximately has a mass of 600 microgramm. So picture the enormous impact of a 50 micrometer long hair falling on a soap bubble.

That said, I can not really tell what is happening in the clip. My guts tell me, that the soap bubble would rather burst than heat up in such a significant way that an upwards force is created. But I am not able to back this up, since I am not an expert in soap bubble surface physics. Also in the world of physics, thermal effects are most of the time rather slow im comparison to other effects, while the bouncing in this clip looks rather instantaneous to me.

So in conclusion, this is either an - admittedly - very good illusion or there is some kind of other effect that I do not see at the moment.