You can hire a good-quality road or mountain bike in Bucharest from a number of places, including those we list here.
However, the cheapest and easiest way of getting your hands on a bike just for ambling around a park is at La Pedale in Herastrau park (where bikes are free for everyone for two hours), or at one of the four I’Velo rental centres located at the entrance to Herastrau, Tineretului and Titan parks. Bikes cost 4 lei per hour, or 15 lei for a full day. The under 16s and over 65s can hire bikes for free (but for a maximum of two hours). You will need ID.