My research as to their activities during WWI are shown below. If anyone knows additional or contrary information, I would be pleased to receive it.
When mobilized, the Staff, 2nd, 3rd, 4th and 5th Squadrons took to the field with the Bavarian Cavalry Division. These squadrons, still in the 5th Bavarian Cavalry Brigade, served with the Bavarian Cavalry Division throughout the war, except for the short period when the division had no cavalry, discussed below. In addition, during September 1914, the regiment was loaned to the Stantz Army Detachment (whereabouts and activities unknown). The 1st Squadron remained behind as the Ersatz Squadron at Bayreuth, 3rd Bavarian Corps District.
The Bavarian Cavalry Division took part in the western campaign until 24Nov1914. Then, the division served as occupation troops in Belgium and trained until 19Jan1915. The 1st and 2nd Royal Bavarian Heavy Cavalry Regiments improvised a Schutzen battalion of four companies, by seconding 80 troopers per squadron, which fought from January to March 1915 at Verdun. From 2Apr1915 until 1917, the division was on the Russian Front, from 16Nov1917 onwards in Romania and from 1Apr1918 onwards in the Ukraine. From 25Nov1917 to 21Mar1918, the division had no cavalry. From 20Apr1918, the division only had two cavalry brigades; the 1st Brigade (1st and 2nd Royal Bavarian Heavy Cavalry) and the 5th Brigade (1st and 6th Royal Bavarian Chevaulegers). Whereabouts and engagements during the period of absence is unknown. In Spring 1918, the division served as occupation troops in Romania and the Ukraine. In early summer, elements were on the Crimea. Both of these brigades remained mounted until the end of the war.
Sources:
1. Volume 7--German Divisions in World War I, Volume 7: Cavalry Divisions and Brigades, by Dirk Rottgardt.
2. Histories--Histories of Two Hundred and Fifty-one Divisions of the German Army Which Participated in the War (1914-1918), by United States Army American Expeditionary Forces General Staff, G-2.
3.Wikipedia.
4. Headgear--Imperial German Headgear (1888-1914) Field Guide, by James Turinetti and Albert O’Connor