From what I could find, the Schiller doesn't have trill keys. Probably why it doesn't show on Dr Potter's list--she won't bother with it if it has no trill keys.
They aren't just for trills, as you use the to help stabilize notes, help more problematic notes sound, all sorts of alternate fingerings. I use mine all the time jumping to a mid-range E or F, both of which don't always sound clearly (of course, this could be due to my not playing bass consistently--or any specific flute, for that matter--see arsenal listed below
My advice, which comes from many MANY emails with Dr Potter (before I knew she was Somebody
and not just a avid low flutist) is continue saving your money, while haunting every possible used flute place hoping for a good brand that includes trill keys. I got my treble from a guy in a facebook group-- https://www.facebook.com/groups/flutes4sale/
. You can post on Dr Potter's facebook group-- https://www.facebook.com/groups/458318884193142/
and see if anyone's heard of a bass for sale. Watch the want ads (where I got my good silver Gemi picc) and Craig's List and the online used flute sites and new flute sellers like WWBW (they sometimes have used, or also seconds). Even eBay, although you need to be aware there's folks who find flutes at estate sales then flip them on eBay and have zero idea of condition, so the cost of the horn might only be a starting point.
Do stay away from the cheap horns, like the no-name Chinese. As pied said, they might start out fine, but they tend to break down and typically aren't repairable.
The main thing is patience. Sometimes an incredible deal will drop into your lap like a gift from on high, when you aren't looking for it. It's how I got my bass--I happened to email Dr Potter at the right moment with yet another question, just after someone local to her happened to email that she was looking to sell her bass.