I'm sorry that no one has answered your question yet. Different experts come on at different times. I just came on and saw your question. Unfortunately, getting a bleeding heart to bloom a second time is hit or miss. It is possible, but unlikely, especially with the old fashioned type. It's often natural for them to go dormant in the summer. If all conditions are right, the plant may come out of dormancy in the fall and bloom again. If your plant is still lush and growing, you can try cutting back the stems the flowers were on. Cut them off where they join the main stem. There is no guarantee, but this is the only way to encourage a second bloom. It may or may not work.
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