Bleeding hearts are more tough than you think. Wait until it is turning yellow and starting to go dormant, then dig it up. Chances are, the root will break apart when you do this so just put the pieces in areas where you want them to grow and you can increase the number of plants you have.

I split mine all the time. They do fine.

I've taken a shovel to my bleeding hearts a couple times to separate them and put them in different spots of my yard, spring, summer, fall, they seem to always survive!
They are amazingly easy to grow.

Here is a link that might be useful: wildflowers/for nature lovers