The issue is still present in Jenkins 2.46.2 and Credentials Binding Plugin 1.11.

I was able to create a minimal repro: https://github.com/mephi42/JENKINS-27040

I was also able to reproduce this in the unit test environment: jenkins-27040-test.patch

org.junit.ComparisonFailure:
Expected :bob/s$$cr$$t
Actual   :bob/s$cr$t

For freestyle projects supposedly this is as designed. (Code in Launcher.) Does not happen in Pipeline.

See JENKINS-40734.

The change from $$ to $ seems to be happening here: https://github.com/jenkinsci/jenkins/blob/master/core/src/main/java/hudson/model/AbstractBuild.java#L935

Sorry, I posted before I saw your reply. Thanks for the information.

Perhaps. Anyway, not a bug in this plugin.

I was able to work around the problem by putting $$$$$ instead of $$ into the GUI. Maybe this information would be helpful to whomever else bumps into this.

Or just use Pipeline, which will behave correctly.

I can confirm that the 5-dollar workaround suggested by mephi42 does work in some cases, but as jglick points out there are many places in Jenkins where variables are expanded.  

For example, the workaround works for a general shell step (some-command.sh -arg "$PASSWORD") but not for a gradle step, where even single-quoted switches like '-Pswitch=$PASSWORD' will again lose the extra $s.  

Pipeline is probably the best solution, but in the interim I found myself having to change the password.