As far as I know, all 3 litre si engines manufactured pre 2008 'can' be prone to the hva ticking if driven repeatedly for short distances then left to sit. As I understand it the oil drains from the cylinder head and doesn't fully saturate the hva's when cold, leading to the ticking noise.
There is a new cylinder head available with a non-return valve to stop this, so BMW recognise it.
Get the car nice and hot, then hold the revs at 3k for a few mins. This is similar to the BMW bleed procedure as a first step to remedying the issue. There is also the option of new hva's, which won't prevent the same happening but may be quieter under the same conditions, then finally the mitigation of the root cause with the new cylinder head.
If the hva's aren't worn, then just changing how the car is used will help. Out of warranty the new hva's and cylinder head are pricey and not necessarily needed.
I read up on this before buying my 3.0si as it was one of the few well documented issues. If you have only just noticed the issue, then my bet would be that it is down to how the car has recently been driven or parked up (1600 miles since Feb is pretty low, esp if lots of short journeys where the oil doesn't heat up), rather than worn or knackered hva's.
Also, check where, what type and when the oil was last changed. I read that the oil grade can have an impact. E.g. 0W versus 5W, or higher, may impact the initial lubing of the cylinder head before the oil heats up. Although it should be fine if oil has been the same since purchase up to the time you noticed the issue.
So most likely more a characteristic of the car, not anything wrong with it, or anything you have done. Loads online, check for N52 lifter tick / hva tick. The E46 3 series shares the N52 so forums for 3series have a lot of info too. Hope you get some reassurance.
Definitely worth mentioning to garage where you purchased it too or a specialist so they can determine if all is well and it's just the way the car has been used recently.