Ian wrote them to ask and they said:
Thanks for writing. Unfortunately without direct access to and from bike trails or light volume traffic routes into the park it would not generally be considered safe or easy for bicycle riders. No dedicated bike racks are available in the park, although if you choose to arrive by bicycle you could certainly lock it to a fence or other permanent fixture. You may need to consult with Park Police or a Ranger on site to be sure you are not in a restricted area.
Which is absolute BS. I've biked out there a couple of times. Here's the route I use. I couldn't find bike parking when I went last year, but Wolf Trap wrote Ian again and said
it has been brought to our attention that a bike rack has been made available this entire summer season for events at The Filene Center. The location is just to the right (south) of the Main Gate before entering the venue.
Which is good because their solution
Metro service via shuttle bus is available for all Filene Center performances
is not true anymore. Maybe they should invest in some more racks and some signage.