In not knowing the configuration of the lights you are looking at, it is hard to answer. If the red light is lower on the vessel around the bridge, you maybe seeing the vessels port side (left) running light. The white light is going to be either a masthead light or possibly a stern light. However if the red light is much higher, atop the mast, then this could indicate more than a few different scenarios.
Lights & Shapes
Rule 21-International
Definitions
(b) "Sidelights" means a green light on the starboard side (right) and a red light on the port side (left) each showing an unbroken light from right ahead (000 degrees) to 22.5 degrees abaft of the beam on its respective side. In a vessel of less than 20 meters the sidelights maybe combined in one lantern carried fore and aft of the centerline.
You are approaching a powerboat head-on
You are approaching a sailing vessel - head-on
You are approaching a powerboat head-on
You are approaching the starboard side of another vessel
You are approaching a powerboat head-on
You are approaching the port side of another vessel
A vessel displaying a visible white light signifies that it is a power-driven vessel. Observing this light helps determine the vessel's status and potential course of action to avoid a collision.
The other vessel is coming directly toward the observer, so both the port and starboard running lights are visible.
The other vessel is coming directly toward the observer, so both the port and starboard running lights are visible.
You are approaching the stern of another vessel and may be overtaking it
Visible Darkness was created in 1959.
It depends on the configuration seen. There are different lights visible depending on the relative headings of the vessels and relative sizes etc.