Since you mention in comments that words like "surface tension and non-newtonian fluids" are thrown at you, I'll avoid using those without explanation in the answer.
The simple way to explain it, without breaking into these dynamics right away (which I don't think is necessary anyways) is to consider the viscous drag, and the buoyant force.
Viscous drag is due to the viscosity of the fluid causing resistance to movement (if you're unfamiliar with viscosity and don't want to try and figure it out on Wikipedia, it's basically how "thick" the fluid feels, how much it resists flowing). In a hand sanitizer mixture, the fluid has a fairly high viscosity, especially compared to water (to see what I mean, try to pour out hand sanitizer without squeezing, it will take awhile if it even wants to come out at all). This relatively high viscosity creates large drag forces which will resist movement of the bubble (it's a bit more complicated than simple drag models, especially for a gel like this; but that's higher level fluid dynamics and perhaps material science).
This viscous drag force would oppose the buoyancy's attempts to move it. Using a simple drag equation we would see a small but gradual movement upwards; as the drag equation only gives a drag force when there is a relative velocity between them. It is possible for the bubbles to flow at a hard to notice crawl. See for example pitch drop experiments where viscous effects can slow things so far that they barely appear to behave as fluids.
I'm not an expert in non-Newtonian fluids, so it's possible that the bubble is able to stop completely due to some higher order effects which the drag equation wouldn't consider. I don't know enough about that to say either way, but it might be beyond the scope of what you wanted to know anyways. Doing a simple search, I believe the effect of completely stopping could be explained by considering the sanitizer as a Bingham Plastic; which can resist a certain amount of stress before yielding; as a Newtonian fluid would to any amount of stress.