I have bullhorns on an old Schwinn I converted to fixed gear, and my one brake lever is inline.
My hands are on the flats, the horns and at the bend (about where hoods would be on a drop bar) depending on circumstances. That is, if I need to get low, I'll reach out toward the end of the horns; if I feel I might need to get to the brake quickly, I stay on the flats near the brake lever. Most of the time my hands are at the bend.
Of course, riding fg, I don't use the brake much, so I suppose where I kept my hands might be different on a geared bike.
I didn't change the stem.