Some Apache committers have successfully run funding campaigns to work on their favorite Apache projects.
This is ok in principle but you have to make it clear that the campaign is your own thing, and avoid any confusion about the role of the ASF and how its projects work.
He's a nice example disclaimer used by one of our committers:
Disclaimers: This campaign is done by me, FOO, as an independent individual, not by the Apache Software Foundation nor the Apache BAR project. I'm not representing the Foundation in any way in this campaign, nor does Apache endorse it. The Foundation has a policy of not paying for development work. All its members are voluntary, me included. Any code I'll write or change will have to pass the usual BAR team approval process. If this campaign isn't funded, I'll continue participating in the BAR project in the same way as before.
See also the discussion thread about this campaign.
If you have any question about this, feel free to ask on our email@example.com mailing list.