Yes, according to Medi Rabbit, all parts of bleeding heart plants are toxic. If you scroll down, you will see it listed on page 5. http://www.medirabbit.com/EN/GI_diseases/Food/Toxic_plants_en.pdf
I found this information from the ASPCA, although they only mention plants poisonous to dogs, cats and horses, so I don’t know if they would have knowledge about rabbits if you call them.
If you think that your animal is ill or may have ingested a poisonous substance, contact your local veterinarian or our 24-hour emergency poison hotline directly at 1-888-426-4435.
I have found bleeding hearts listed as toxic on several sites. This site, the Wisconsin HRS chapter, lists it as a class 2 toxic plant, saying that it may cause an allergic reaction. At least it must not be as toxic as some plants. http://wisconsinhrs.org/wp/wp-content/uploads/2013/08/WHRS-Library_ToxicPlantsList.pdf. They say that you should call your vet to see if a consultation is warranted.