Are there any safety concerns to have an current flow through a bronze wire that is connected to a copper wire?
Electrically, no there is no safety issue, not so long as they can both carry the applied current. That, and it meets safety isolation/insulation requirements.

Chemically you may set up and accelerate galvanic corrosion which may cause the bronze to rot out before it's time, especially at the joint. That can cause an increase in resistance and subsequent overheating or burning out. How big an effect that is will depend on the make up of the bronze and which direction the current flows. Fortunately copper and bronze are fairly similar metals in this department so the effect should be a slow one.