Critiquing-based recommender systems aim to elicit more accurate user preferences from users' feedback toward recommendations. However, systems using a graphical user interface (GUI) limit the way that users can critique the recommendation. With the rise of chatbots in many application domains, they have been regarded as an ideal platform to build critiquing-based recommender systems. Therefore, we present MusicBot, a chatbot for music recommendations, featured with two typical critiquing techniques, user-initiated critiquing (UC) and system-suggested critiquing (SC). By conducting a within-subjects (N=45) study with two typical scenarios of music listening, we compared a system of only having UC with a hybrid critiquing system that combines SC with UC. Furthermore, we analyzed the effects of four personal characteristics, musical sophistication (MS), desire for control (DFC), chatbot experience (CE), and tech savviness (TS), on the user's perception and interaction of the recommendation in MusicBot. In general, compared with UC, SC yields higher perceived diversity and efficiency in looking for songs; combining UC and SC tends to increase user engagement. Both MS and DFC positively influence several key user experience (UX) metrics of MusicBot such as interest matching, perceived controllability, and intent to provide feedback.