BeablossomR_ said:

For those who have studied this before, do you think it’s more helpful to think of it in terms of physics concepts, biology concepts, or a mix of both?

I would say both. The physics aspects show how things work in detail, but an awareness of the biology shows why the physics is applied where it is in their biological manifestations and how it fulfills biological needs. Once the large scale (biological) process is identified, you can build explanatory mechanisms up from the physics to explain particular biological phenomena.

I have always liked the approach of superimposing a schematic cell with the equivalent electrical elements you mentioned. This can also show how different regions of large cells can propagate signals like action potentials.
Things are often shown like this:

but this is only a small patch of the cell's membrane.
A large number of these little patches would have to be put together to model larger parts of a neuron. Here is a simple example:

More complex situations involve branch points, changes in diameter, and changes in the molecular circuit components from place to place. This is even further complexified by considering the many possible synaptic connections with other cells.

Bioelectricity is a term that also includes some other aspects of biological functioning.
The main thing with the functioning of neurons involve the membrane potential (the charge across the cell membrane) and how it can change (by altering the membrane potential in different cellular regions like the cell body, axons or dendrites). These are local changes in little regions of the cell that can cause physiological changes (like release of synaptic vesicles). The membrane potential changes can be transmitted to neighboring regions by various methods (like a propagating change of an axon potential). This only involves negligible current flow to different parts of the cell. In addition, electrochemistry (a physiological term for trans-membrane electrical properties like action potentials) is also important in how kidneys work to remove wastes from the blood, but retain electrolytes and water.

An alternative way bioelectricity is used is where actual current flow (probably ion flows) go in and out of different regions. Different methods are used to study these phenomena and they are connected to different biological events. Current flow out of amputated limbs are often observed. Some connect them with success or failure of limb regeneration. Whole body current flow has also be linked with body plan establishment in planarians. Sensitive probes have also been able to detect current flows coming out of cut axons.