I would say as a rule, depression and anxiety do not cause bigeminy, but bigeminy can certainly cause anxiety and depression.
Runs of bigeminy often lead to other flavors of arrhythmia. In my case, it causes mild tachycardia, pretty mean bradycardia, and an occasional block.
I also like what dolfnlvr said about arrhythmia and death. I will add that there is a catch 22 in bigeminy and other arrhythmias being the cause of death. I suspect bigeminy is never blamed for death because it disappears at or shortly before the time of death. I think it can certainly be implicated, but it would be hard to blame directly.
This answer was something I've posted before, so I cut an pasted it into this thread. Hope you don't mind the "repeat."
Every cell in your heart has the capability of initiating a contraction. Most don't, and that "chore" is relegated to the SA node or your "natural pacemaker." These specialty cells begin an electrical signal that causes all of the cells in your atria to contract, and the electrical signal reaches your ventricles which then contract a fraction of a second later. Adrenaline and other chemicals are part of the endocrine system, and their job is to increase heart rate when you are afraid (fight or flight). This chemical causes the SA node to fire more frequently increasing heart rate. SOMETIMES, regular cells in your heart can become sensitive to adrenaline and others and they sort of try to "help out." Thus, initiating a contraction that is "out of sync" with the others. In the case of PVC's the source of these ectopic beats are cells in the ventricular area, with PAC's they are in the atria.
One common denominator in ectopic beats is the adrenaline response. That is why cardiologists often prescribe beta blockers as a first step in helping to alleviate symptoms. The beta blocker "blocks" some of the adrenaline from being detected by the cardiac cells and therefore decreases the number or at least the force of the ectopic beats making them less noticeable. Interestingly enough this sets up a negative feedback loop. Your heart beat does not frighten you as much, you don't produce as much adrenaline AND what you are producing is still somewhat "blocked." So, your heart beat calms...and you worry even less, which is less adrenaline and so on and so forth. Sometimes doctors will pair a prescription of Beta Blockers and an SSRI (Paxil or Prozac as examples) in low doses to lower the anxiety levels of those experiencing the ectopics. This is not because the PVC's are in your head, or because you are weak, or because you imagine them or are crazy. This is purely to reduce the effects of the positive feedback loop that feeds ectopic beats. If you worry, you become anxious, if you are anxious, your body produces and releases adrenaline...which increases ectopics, which increases worry. It is biological.
As for "how do they know it won't kill you." Well, no-one knows when their time will come. All of us are living on borrowed time, we just don't know how much time we have. However, in the case of PVC's and PAC's research has shown that people who experience these beats are statistically NO MORE LIKELY to die of sudden heart attack, heart failure or other cardiac causes at an early age. There is a SLIGHT, but negligable, association of persistant ectopics (upwards of 10-25,000/day) causing cardiomyopathy. This is not a common situation however, and if you are under the care of a cardiologist who will check on your symptoms usually annually, this is unlikely and if it does happen is treatable. So...statistically speaking, hundreds of thousands of people experience PVC's (most with absolutely NO sensation of having them) and their cardiac induced mortality is no more than those who do not have the ectopics.
Take care...