Women - one aged 80 - attacked on bus
The female suspect got on a bus travelling from Wirksworth to Derby at about 7.30am on Saturday.
During the journey, she assaulted the 80-year-old woman - by banging her head on a seat.
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Hide AdWhen the bus reached Belper, the offender stepped off then attacked a second woman by pushing her to the ground.
The offender then continued her journey to Derby.
She is described as white, in her mid-20s, with shoulder-length dark hair. She was wearing a tracksuit and multi-coloured socks and was carrying a Nike sports bag.
Police believe both attacks were unprovoked and are investigating.
Anyone with information should call PC Matt Moore on 101, quoting incident 181 of June 25.