fastest B field rise time in an inductor/electromagnet
For me there are multiple smaller paralleled inductors all driven with
  the same signal, so the inductance will be very low.


If all those inductors are wound on the same magnetic core and have the same number of turns then they will behave pretty much like one inductor made of thicker copper wire. In other words, due to magnetic coupling between them, the net parallel inductance will be hardly different to the inductance of one coil.


  I know that this is largely dependent on the inductance of the
  inductor.


Correct, when applying a voltage pulse, the current will rise at V/L amps per second. Paralleling many inductors on the same core will not make "L" any smaller theoretically.


  Do Ferrites have better parameters with regards to this.


They will have fewer losses at higher frequencies but, at the end of the day inductance is the limiter of speed so, to counter that you need to apply a higher voltage but, current will ramp all the same. Current does not "follow" voltage for an inductor.


  Does the B field rise curve follow the coil current rise?


It does.