I'm almost certain there must be an interlock, cause if there isn't, you'd probably end up having a nasty Hot Start.

There are more than just A320 APUs that create contaminated air into the bleed air and packs if started and immediately have the bleed/packs switched on.
The A330, 340 and 380 that I have flown, will also generate the smell of sweaty socks or smelly running shoes through the air conditioning and this is the definitive symptoms of oil leaking into the compressor section through the labyrinth seals and being heated and turned into the accumulative toxin in the oil fumes. Moving Jet II oil is the problem due to its additives.

So the big picture is your health danger of the accumulation of these oil fumes over a long career, known as Aerotoxic syndrome, google it. My specialist told me 60% of people are unable to detoxify this synthetic oil fumes toxin.

All pilots should learn early what the oil fumes smell is like and take whatever steps to avoid it including delaying Packs on in this procedure and encouraging your company to adopt oil fumes mitigation safety over absolute minimum time from APU start to packs on.

I am an oil fumes incident survived and urge you to take it seriously.

Our FCTM says that Airbus SOP is to select the bleed on straight away. They then go on to say that waiting 3 minutes can help reduce oil fumes.

On our fleet we do notice a significant reduction in odour events, after we started observing the 3 minutes waiting time before putting the APU Bleed on.

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If you're on a multi leg day, with 50 mins turnaround, can you consider that the APU is still warm from the previous start ?

Indeed it is Airbus SOP to use APU Bleed "when the APU is AVAIL" (FCOM PRO-NOR-SOP-04 P 4/12). However, FCTM PR-NP-SOP-40 P 1/4 states (company with non-customized manuals, my highlight):

While you can use APU bleed straight away (otherwise it would be in the limitations section), my interpretation of this is that it is indeed beneficial to delay its use for 3 minutes after APU start for the reasons mentioned above. Beneficial, but not mandatory or even SOP. We might just call it something like good operational practice, whenever feasible.

I tried to do follow this "practice", particularly on the first APU start of the day, pretty much like someone mentioned previously: start the APU, start the timer when AVAIL lt on, do something else in the meantime, then set bleed on. Mornings are quite cool most of the year at my base, so I'd take further advantage of that and just use one pack all the way until takeoff if the temps in the cabin were comfortable.

Now, something I didn't take into account is the effect of the (short, usually less than 1 hour flt time) flight had on the APU temps for the next flight, as I didn't follow this said practice for subsequent flights. Anyone with any info about this?

I think I remember in the really early MSNs you would wait until the "Flap Open" indication on the APU SD page before pushing the start PB. However, after about MSN 25xx or so (in that particular company fleet) you would only need to wait 3 seconds after pushing the APU master PB. APU ECB won't let it start before the flap is open.

I can confirm the inlet flap / starter was a technique shown and agreed upon at my operator for the -3/4/500

Upon change to AB at 2005 no such trickery needed. ECB what comtrols the sequence, innit? MSN 960 and above (older, leased ships).

What's the problem with trusting your MX AB representative, APU supplier support team and the FCOM guidance? Serious qusestion, there seem to be one.