Here's how it's done...
Step 1: Starting with Serum’s default preset, head to its first oscillator (Osc A) and call up a sine wave. Set its Random Phase to 0%, so the wave’s phase resets every time, then shift its Phase to 60 degrees. This starts the sine from midway through the waveform, giving us an initial click.
Step 2: Serum’s Envelope 1 is hardwired to amplitude. Unlike a booming 808 kick, a punchy, house-esque bass drum is typically tight and short, so pull Sustain to minimum before setting Decay to a tight value of around 520ms. An Attack value of 0.2ms brings out that click a bit more.
Step 3: Now it’s time to sweep the sine’s pitch from high to low with an envelope, which will create the distinctive punch we need. Head to LFO 1, flip it to Envelope (ie, one-shot) mode, then drag the existing node fully left to dial in a downwards ‘fin’.
Step 4: We’ll come back and tweak this shape later, but for now, assign the LFO to modulate Osc A’s pitch by dragging LFO 1’s target cross and dropping it on Osc A’s Coarse Tune slot. Switch this modulation from bipolar to unipolar by Shift-Alt-clicking on the mod destination slot.
Step 5: Now you can shape this rapid pitch fall to design the type of bass drum you want. Drag LFO 1’s central node downwards to bend the straight line into an exponential ‘spike’ shape, then tweak the amount of LFO-to-pitch modulation.
Step 6: The interaction between pitch mod amount and the modulator’s shape will determine the kick’s pitch ‘bump’. Generally, the more languid the curve, the more of a 909-style ‘punch’ you’ll get, whereas tighter mod spikes sound more 808-esque.