Does the transformer or the bulb determine electrical bill?

The answer is (1). Your electrical consumption is determined by the actual power used. Three 5oW bulbs will consume a total of 150W, of course, and added to that will be a small amount of heat dissipated in the transformer (no transformer is 100% efficient) but this will be very small, a few percent so the AC input draw to the transformer might be (say) 155W probably less. (Does it get warm?)

The rated output of the transformer is simply the maximum amount of power you should continuously take out of the transformer to remain within the manufacturer's temperature limits. You are running the transformer at 50% of its rated load, which is a good thing.

Yes, it does get warm....noticeably warm. It is a Malibu 600W (two 300W legs) transformer, with roughly 100W on one leg, 200 on the other. I am considering moving the transformer to both shorten the wire run(s), and attempt to get 150W on each leg. It's the heat being generated that caught my attention and started me questioning things. Thanks for you assistance.