I was not able to find other elements to confirm
1- Had he ever had the bleeding heart painted on his plane?
2- If so on which plane?
3- If it was a SPAD was it a VII or a XIII?
1 - Here is what
Greg VanWyngarden says in the Aerodrome :
Many years later, Bullard is said to have stated that he flew a blue 'SPAD' with a personal red bleeding heart emblem (stabbed with a dagger), with the legend "Tout sang qui coule est rouge” (All blood runs red) written surrounding it. So it could be just a story he talked about after returning home, but (Greg VanWyngarden again):
Jon Guttman wrote an article about Bullard in “Windsock” magazine, and Ray Rimell did a colored profile of Bullard’s Escadrille 85 Spad VII based on Jon’s directions. 
I don’t know on which basis Jon and Ray have produced this profile, although the scheme is provisional and based on Bullards tale.
There is no photo of Bullard’s plane with the bleeding heart but a fake one which was touched up replacing the Indian’s head of the Lafayette corps with a modern drawing. See the type of character used for the motto, it’s something like ARIAL, and the rigging shadows on the fuselage appear cancelled, and in any case the plane is a Nieuport.
ORIGINAL (found here:
https://tacairnet.com/2014/06/03/raoul-luf-lufbery/ )

FAKE

There is also this image here (a SPAD) but the bleeding heart is exactly the same of the previous photo, it seems cut and paste from one pic to the other

2 - According to what Greg VanWyngarden says in the Aerodrome he flied mainly Ni 24 because SPADS arrived to his Squadrons after he left. But I read that SPAD XIII started being used by the Armée de l'Air in May 1917, the Escadrilles assumed the prefix SPA when most of the machines were of that type, but this does not meanthat when called N an Escadrille had only Nieuports, maybe it could have a few SPADS...
3 - SPAD VII or SPAD XIII (I have no clues on this but the profile published by Ray Rimell)
I also bought as E-Book “Eugene Bullard – world’s first black fighter pilot” and will start reading it in the next days.
I would like to read your opinions on this!
Thanks
Antonio