The issue here is that cycles, which uses backwards path tracing (tracing light rays from the camera to the light sources), is not very good at rendering caustics in these kinds of situations.
This is because it's not very likely for a ray to bounce off a surface, transmit through the glass bulb, and hit the element within. Multiple Importance Sampling (MIS) usually helps with this by guiding more rays to hit light source(s), however the glass bulb surrounding the light source effectively prevents this from working.
From left to right: Element with MIS, Element without MIS, Element with MIS and glass bulb.
To properly render such a situation, solutions like Bi-direction path tracing and Metropolis Light Transport (MLT) exist. Unfortunately, cycles does not yet have this functionality, and it is considered "not a priority" according to the cycles roadmap.
Even so, there is a working patch for MLT (and adaptive sampling/stopping) which is being actively developed as of the time of this posting. You will have to compile blender yourself (it's really not hard) to use this patch.
There is also an older patch for Bi-dir here.
Here is an example render of the element and bulb with the MLT patch:
It's better, but not at all the desired result (I don't really know any of the MLT related settings yet, so it's possible this could be improved some more).
- Use a point lamp for doing the actual illumination, and make the bulb and filament only visible to the camera by mixing the glass or emission shader with a transparent shader based on the is camera ray output of the light path node.
There are a few things which can prevent indirect bounces from transmitting through objects entirely:
Make sure No caustics is disabled and any lamps which you want to shine through or reflect off transmissive or glossy materials have MIS enabled.