I am confused with inrush current. I am driving a motor and i am protecting my circuit in case of high DC bus current by monitoring it. What is the safe time limit in which i should be able to detect this current? Is it correct that every time motor starts there will be inrush current? If that is correct then how to avoid falsely detecting the inrush current as high dc bus current?

 

The initial current for a DC brushed motor is limited only by the actual resistance of armature coil and brushes.
Once rotating, the generated DC opposes the applied voltage, decreasing the current.
Max.

 

The inrush of some DC motors can be shockingly high, depends on the armature resistance of the motor.
You need to design for this current, ignoring it will have consequences.

 

You could try a soft start by ramping up a PWM driver on the motor at startup. Otherwise, as Sensacell mentioned, design for high current as it will be needed. It is always a good idea for a motor drive to make the supply pretty rugged, otherwise a motor stall will destroy stuff, with a good show of smoke!
Years ago, my workmate had great delight in sitting on the electric bike I made a controller for, jamming the brakes on, and wrapping the speed control on full. BANG!! Very impressive with smoke coming out from under the seat one was sitting on, as that is where the speed control was.
The final design had current feedback controlling the max current by PWMing the drive so it would not kill itself. So the rider could wind the throttle full on and the bike would accelerate smoothly away.