Okay so I have realised that the bulb fading is more likely caused by the bulb itself, beacause it also takes a little time for the bulb to turn on. Since it is a filament bulb this makes sense (to me) that it takes a considerable amount of time for it to heat up and cool down (in order of tens of miliseconds), so it probably compensates itself and shouldn't be a problem even with short exposure times (though I haven't tested this yet). This came to me after realising how capacitors behave in an AC circuit.
I feel stupid now after posting the previous reply, but maybe this revelation will help someone. Or I got it wrong and someone will correct me.