I once spent several years researching bubble machines and am attaching a diagram of the fruits of my labours. You will probably have trouble understanding it, but it is supposeed to be a disc made of stencil card with an overall diameter of 14 inches. I found it was a good idea to re-inforce the rim with a thin steel guitar string 'sown' into it.
The one in the diagram is turned by hand with a margarine tub bolted to it but I also made a motorised one (see below). Three concentric rings of holes works better, but then it gets a bit big.
This design has the advantage that you can use any old washing up liquid. It makes lots of bubbles all at once which solves the problem of the bubbles closing: many of them burst but the survivors merge together into large bubbles. The holes in the card are about one inch diameter. The one in the diagram is supposed to be overhanging the edge of a table, someone else has to hold a desk fan underneath.
Motorising it is quite difficult; someone gave me a fairly hefty dc motor/gearbox to which I attached a meccano wheel, I then bolted the margarine tub lid to the wheel. I supported the motor/gearbox with bent wire, I used fairly weak wire so that in the event of the wheel jamming the wire gave and not the wheel.
The motor/gearboxes are quite expensive, it has an epicyclic gearbox which tends to jam. It takes a lot of turning force to turn the wheel.
One of the few hard & fast facts of child psychology I have ever been able to pin down is they love bubble machines.