Unless the inmate is medically incontinent then no the inmates do not wear diapers when being transported to prisons or transported from one prison to another prison etc.
Even long distance prison transports the inmates are either expected to hold in their urine or feces or wet or soil themselves as the driver and prison guards nor do the prison system care whether an inmate soils themselves on the ride when being transported to and from prisons.
Other inmate trustees do the cleanup anyway so they would not care and most prison inmates do just soil themselves if they cannot hold it especially on long distance prison transports.