I bottle, I dry hop loose and I do not cold crash. So I'd say I'm in a very similar starting situation as you.
Usually by the time I bottle, I've got most of the hops settled at the bottom, but with some significant portion still floating on top.
During the transfer I try to keep the tip of the racking cane a few cm below the surface level, that way I'm sucking up little hop material, at least until the last few liters.
I also place a deep monofilament filter bag in the bottling bucket, something like this for example:
https://www.candirect.eu/Monofilament-filter-bag-150l-size-2-175-liters
The bag reaches the bottom of the bucket, so the beer won't actually be exposed to more oxygen as in a "normal" transfer without this filtering step
(The bag remains submerged in the beer during the transfer, there is no splashing around and such).
This will stop virtually all but the finest dry hop particulate from landing into your bottling bucket.
This is how I do it but as said above, there are many ways to tackle this issue.
For instance, I know that most NEIPA bottlers would strongly advise you to bottle directly from the fermenter. This is probably the best practice with respect to minimizing O2 pickup. Then on the other hand, it is almost impossible to do this without either a thorough cold crash to settle the hops, or bagging the dry hops (which IMHO diminishes significantly the flavor- and aroma extraction...). And a cold crash can also bring its own oxidation problems if you cannot do something about preventing air suckback.
