Relativistic Light Speed in a Bubble

[Walter The Moral]

Do we think that the speed of light in a speed bubble is the same for someone inside a bubble as it is for someone outside?

How could this be checked? The only way I can think of is putting a speed bubble inbetween two mirrors, and measuring the number of times the light bounces off each mirror. This same experiment could be conducted from inside the bubble, and the speeds could be compared.

What consequences would this have? We already know that there's some magic which prevents Blue and Redshift from happening, but what other things could be caused?