In this case they mean the same thing. The "me" makes the construction reflexive, but in this particular case the meaning doesn't change.
The verb
aburrir means
to bore, which is something you can do do somebody else:
¿Te estoy aburriendo? = Am I boring you?
While
aburrirse (the reflexive form) means
to get bored, which is an action entirely isolated to yourself.
Me estoy aburriendo = I'm getting bored.
Often when you make a verb reflexive (by making the recipient of the action the same as the subject), the meaning of the verb can be thought of as the English
to get + verb.
For example
to bore vs.
to get bored, though this is just a guide if you can't find a real definition for the reflexive verb. Some verbs change meaning entirely when made reflexive, so you should always check a dictionary to be sure.
Because the construction you posted uses
estoy + the past participle, it can only ever apply to yourself though, so the reflexive version is basically the same
Read up on reflexive verbs:
http://spanish.about.com/od/sentence...xive_verbs.htm