Bubble up is the name of a soft drink, but at Microsoft, it means something else. (Remember, Microspeak is not just terms used exclusively within Microsoft, but also terms used at Microsoft more often than in the general population.)
To bubble up information is to expose the information at a higher reporting level. For example, you might have a local team report that goes into detail over all the work items the team is responsible for and the corresponding status of each item. The data from this report may bubble up into a group report, which summarizes the work item status across all teams.
As another example, if there is an error condition in a particular item, the error may be reported on the status page for that item, and it may bubble up to the status page for the container as well (meaning that the information will be reported there, too).
Information can bubble up in other less formal ways. For example, your manager may say, "That's important. "I'll make sure to bubble that information up in our weekly status meeting," which is a jargony way of saying, "That's important. I'll make sure to present that information in our weekly status meeting."
The implied metaphor is bubbles rising to the surface of a liquid, with the suggestion that reaching the top of the liquid is a good thing in some way or other. (Even though people usually don't pay attention to the bubbles at the top, and once they get there, they tend to just hang around for a while, and then pop. A rather ignominious end to a bubble, if you ask me.)
The concept of information flowing to higher levels is used even in the HTML DOM specification: Event bubbling is the term used to describe how an event travels from an element to its parents.