Transistor has the answer; here's some background info and one solution.
That's a common question we get from novice electronics guys -- they think about how residential AC light dimming works, and figure
- It can't be an inline resistance; that would make a lot of heat.
- It can't be a variac; since those are huge.
Transistor (above) describes the triac and diode dimming.
Now, you say "non-dimmable bulb" -- the photo you have is of an incandescent bulb, which is nothing but a resistor with some weird properties, not least, light emitting lol). So dimming is inherent in all incandescent bulbs, and triac dimming is specifically designed to be a cheap solution to dim incandescents. It will play nice with diode dimming too.
My point: All this goes out the window when you start dealing with alternate lighting tech such as compact fluorescent or LED. Because heat is a concern, they use a switching power supply to make the correct current for the series string(s) of LED emitters. That is typically multi-voltage (like 90-264V, world voltages +/-10%) and dynamically adjusts to input voltage so fast that it can ride through triac dimming. It treats dimming like dirty power lol!
Dimming fluorescent is ...complicated... and triac dimming just gets in the way. LEDs can dim either by reducing current through the emitters or by PWM. Triac dimming doesn't do that, so the "dimmable" LED/CFLs have a circuit to reverse-engineer what the triac dimmer is trying to do, and then do that. Obviously that is extra complexity/cost.
I expect the "simple diode" dimming method is not one that these modern bulbs know how to emulate. Your best bet might be to fill the bowl with LED Christmas lights; those are typically wired in 2 series strings of LEDs, with each string facing the opposite direction, so each string lights up half the cycle. In your lamp, at the "dim" setting, one string would light.