im pretty sure they wont let you in a bath if your being induced (gels) and once synto is on they will have you monitored pretty well constantly.

perhaps call the hospital and ask what their procedures are in regards to induction, then you can decided exactly what you will and wont do..
i agree. Once they begin the induction, your ability to have an active birth is limited. hospital policy is largely the limiting factor so get as much info beforehand so you are prepared. high blood pressure can mean they will want constant monitoring. depending on the shape of your tummy, it can be hard to keep the monitors on where they can read bub, whilst getting in different positions.

good luck