odubov has good experience with bluetooth devices and FM. Using bluetooth directly to iOS you need a listening app that will send data back to FM.
First issue is managing the signals. I am assuming that one doctor will have many devices to interact with. Storing all the data from all of them via bluetooth to one iPad may not be possible unless each patient is assigned an iOS device to collect their data and then that is uploaded to the server (Apple Watch with iPhone is a good example of this). Might not be the best ideal for more than two devices at once. If you just need data from a short test this becomes more manageable. But you still need the operator to pair with each monitor.
Most hospitals have some sort of main EMR/EHR system/database. If those systems have an API to access data you might be going in the right direction there.