Cumbria Police said the bus driver was arrested on suspicion of dangerous driving after Monday's crash in which four adults and several children were injured, none seriously, The Independent of London reported.
"At this stage, it is too early for us to confirm the number of casualties, but we believe this to be in the region of 20 people," an emergency services spokesman said.
Cumbria Police said told the BBC the bus' passengers included school children between the ages of 13 and 16.
"No child has been seriously injured," police said.
The cause of the accident was under investigation.