So how deep are the bubbles? And how did you cast this? Did you put billet in the box mold, or drip it in from a reservoir above the mold or...?
Yes, you can refire and hold it longer, possibly at a slightly higher process temp, until the bubbles rise completely to the surface, pop and subside. For bubbles like that I wouldn't do the pop-and-add glass method--that could trap more air. The refiring by itself should be sufficient to clear the big guys out.
Refiring doesn't work that well if you have multiple color layers, because the rising bubbles pull the colors up, leaving a trail. Since you appear to be using all the same color in the casting, that shouldn't be a problem.
One thing to watch out for, though: Smaller bubbles, farther down, will start rising while you're resolving the surface bubbles. They may hit the surface too, or group to become big bubbles themselves. You'll need to give them time to rise, pop and subside, too. When I say "hold it longer," I mean until all bubbles have resolved. That can take hours, depending on the piece, the temperatures you're using, and where the bubbles are trapped. And the longer you hold the temp, especially with soda lime glass, the more chance you have of overheating the glass, causing devit at the edges, etc. It's a bit of a balancing act.
Smaller bubbles won't rise easily--they have to overcome the viscosity of the glass and surface tension--so they're more likely to stick around. If they're really small they'll be tough to dislodge. (We call those "evidence of hand-made art")
