Yeah, not the best choice, then. "Bleeding heart" has been used as a slur by (US political) conservatives[1] to attack (US political) liberals. It implied that the liberals suffer from an excess of empathy to the point that it clouds their judgment, or something. Nowadays it's just a slur.
You're using "liberal" in a way that differs from standard US political usage, which is all right, especially since you clearly defined what you meant by the term. But "bleeding heart" sounds very US-politics, and seems really weird with your not using liberal in the US politics sense.
[1] These "conservatives" would count as liberals by your definition - they still believe in individual rights.
Frankly, I have only heard liberals self-identify as "bleeding heart", and misunderstood its definition. Then again, I don't consume US conservative media.
> These "conservatives" would count as liberals by your definition - they still believe in individual rights.
Of course. Virtually every faction of US politics is philosophically liberal.