Deoxyribonucleic acid (DNA) is an essential molecule that enables the storage and retrieval of genetic information. In its role during cellular processes, this long flexible molecule is significantly bent and twisted. Previously, we developed an elastodynamic rod approximation to study DNA deformed into a loop by a gene regulatory protein (lac repressor) and predicted the energetics and topology of the loops. Although adequate for DNA looping, our model neglected electrostatic interactions, which are essential when considering processes that result in highly supercoiled DNA including plectonemes. Herein, we extend the rod approximation to account for electrostatic interactions and present strategies that improve computational efficiency. Our calculations for the stability for a circularly bent rod and for an initially straight rod compare favorably to existing equilibrium models. With this new capability, we are now well-positioned to study the dynamics of transcription and other dynamic processes that result in DNA supercoiling.