I'll often send a tell to the private runs and ask them if they expect to be short an arcane, bard, or tank. Having all 3 of those capped at the moment I've had a few times where the private LFM's were suddenly not so private anymore when I asked about their needs.
As an aside, those 'being choosy' raids - they're not so choosy when you hit them up with a pure bard. I think the bar on Bards basically amounts to the following 3 questions:
1) Are they a known idiot?
2) Is their build idiotic (staying pure is a guarantee to get a pass here even if you completely screw the toon up )?
3) Do you have enough hp's? If they myDDO you make sure your hp is a high number. It doesn't matter if your myDDO shows you using a Club of the Silver Flame, if you've got 500hp's you're in.
Obviously bad bards will eventually hit the #1 list. That said, I grouped with someone I don't remember ever grouping with on a recent 'being choosy' ToD. I hit the LFM and was IMMEDIATELY accepted on my 20 pure bard. That's not very choosy.