Some ultraluminous X-ray sources (ULXs) are surrounded by collisionally ionized bubbles, larger and more energetic than supernova remnants: they are evidence of the powerful outflows associated with super-Eddington X-ray sources. We illustrate the most recent addition to this class: a huge (350 pc × 220 pc in diameter) bubble around a ULX in NGC 5585. We modelled the X-ray properties of the ULX (a broadened-disc source with L_X ≈ 2–4 × 10^39 erg s^−1) from Chandra and XMM–Newton, and identified its likely optical counterpart in Hubble Space Telescope images. We used the Large Binocular Telescope to study the optical emission from the ionized bubble. We show that the line emission spectrum is indicative of collisional ionization. We refine the method for inferring the shock velocity from the width of the optical lines. We derive an average shock velocity ≈125 km s^−1, which corresponds to a dynamical age of ∼600 000 yr for the bubble, and an average mechanical power P_w ∼ 10^40 erg s^−1; thus, the mechanical power is a few times higher than the current photon luminosity. With Very Large Array observations, we discovered and resolved a powerful radio bubble with the same size as the optical bubble, and a 1.4-GHz luminosity ∼10^35 erg s^−1, at the upper end of the luminosity range for this type of source. We explain why ULX bubbles tend to become more radio luminous as they expand while radio supernova remnants tend to fade.