Is there a word or expression to describe a really bad computer bug?

You can use an array of words, such as; terrible, horrendous, awful, horrible, and others.

I recommend consulting a dictionary any looking for synonyms of the word bad, or any words similar to it. Here is a useful resource in this regard.

Words such as “critical” are used informally in -as you’ve observed - fairly meaningless ways. However, they also have formal definitions in many situations.

A service agreement will define the meaning of “critical” and similar words precisely. A service agreement I signed defined “critical” as “severity level 1 or 2”, with severity levels running from 1 (significant and ongoing interruption; unrecoverable data loss) to 4 (general questions and wishes). Obviously I can’t cite this agreement for legal reasons, but if you Google for service agreements, you’ll find examples.

These rankings are not universal, but would be specific to a company or agreement. Consideration is often given to the proportion of users impacted, whether data is lost/corrupted, and whether the functionality impacted is “core” or not.

A company I worked for previously ranked defects from 1 to 3 (plus “as designed” and similar non-issue classifications)

For security issues specifically, CVSS scores are widely used.

These formal definitions avoid issues of inflated language like “absolutely awfully terrible, literally the end of the universe” bugs. When communicating to management about the severity of an issue, formal definitions are good to use.