Do you get a deployment patch for a 3 month training rotation to Bulgaria?

The time spend in a combat zone don't matter to obtain a combat patch SSI so 3 month 30day even 1 day ok however a rotation to Bulgaria isn't combat zone so those guys shouldn't be wearing it

I do not think they will be wearing them for long as a combat patch.

First read the regulation on authorization to wear a combat patch. Second, did the unit get orders authorizing the wear of the patch? There is your answer

Are you sure they are not pulling your leg. There is no sort of conflict in Bulgaria that warrants a service patch. There may be some local policy allowing Soldier's to identify with something for a period of recognition. While not IAE policy, it may be done. I would ask a senior leaders what they are.

"The Shoulder Sleeve Insignia Former Wartime Service will now be called the Shoulder Sleeve Insignia Military Operations in Hostile Conditions. It is authorized for soldiers who served on combat deployments to Iraq and Afghanistan, but also those who served in certain countries considered hostile areas.

"Sometimes, we go to certain locations, and we don't plan on that to be hostile conditions, but it may turn hostile," Sergeant Major of the Army Michael Grinston said. "How do we recognize those soldiers who are out doing what we have asked them to do? ... So we allow them to wear the shoulder sleeve insignia for the unit. I think that is appropriate."

The new shoulder sleeve insignia is currently authorized for Somalia, Djibouti, Saudi Arabia, Iraq, Afghanistan, Pakistan, Yemen, Jordan and Syria."

https://www.military.com/daily-news/2021/01/27/army-rolls-out-army-green-uniform-wear-guidelines-renames-combat-patch.html#:~:text=The%20new%20shoulder%20sleeve%20insignia,optional%20undershirt%20designed%20for%20nursing.

But - that's currently. I don't know when these people went to Bulgaria or if it may have been authorized at some point without doing some research into it. I would say 'no." Did they say that is what it was for?

It may be possible but it wouldn't have been for a training exercise or TDY. This NG unit appears to have gotten theirs for Bulgaria:

"Additionally, the Department of Military Affairs says in 2002, following the 9/11 terrorist attacks, the unit was deployed to Europe as part of Task Force Santa Fe, in support of Operation Enduring Freedom. Soldiers with the 2-130th became the first United States troops to train in Bulgaria after the previous Soviet Bloc nation was accepted into the North Atlantic Treaty Organization " But that was in 2002.

I don't think this is what the article is about I pulled that from but if it was part of something for OIF/OEF maybe? But it doesn't sound like it. Ask any leadership if there's orders for it.

https://www.wpsdlocal6.com/news/deployed-illinois-army-national-guard-soldiers-receive-combat-service-patch/article_896a8a90-e3c6-11ea-bb61-bbeae091df3d.html