On the other hand, instead of DIY you could just buy air purifier units with integrated air quality sensors. A friend of mine uses these, they appear to work very well https://www.philips.co.uk/c-p/AC2936_33/2000i-series-air-pur...
I would not recommend it purely because they decided to use an extremely poor touch interface for control which quiet often doesn't register when I try to manually adjust something like shutting the unit down temporarily or resetting an error code
Buying a purifier that can fit standard sized “box” filters will save you $$ in the long run.
Having one very powerful air purifier hidden away in another room is not as good as having a bunch of smaller ones spread around.
Overall, yes, a cheap box filter (placed specifically in the bedroom, if limited to one room) is often the most effective.
Speaking of expensive air purifiers, you can often find excellent deals on used IQair units. I got 4 GC Multigas units from a local museum for 100 euros each.
I have an alert set up on the local craigslist equivalent and constantly get emails.
Those filters were used though, no idea for how long (they only had like 70 hours on them according to the onboard tracking, but that would be easy to manipulate even by accident)
This essentially tracks with the numbers presented here https://www.iqair.com/newsroom/why-you-need-to-replace-your-...
IQair recommends a yearly replacement for my HEPA filter, but my environment had a fairly low amount of particulates to begin with (new building with filtered air intakes) and workload split between multiple units.