It all depends: - the size of the engine, size of bird, etc.
If you are aware that a bird has been through the engine then the safest action is to land and have the power-plant thoroughly inspected. Irrespective of the flight time required to an appropriate airport the subsequent actions will depend on the engine indications.
If you smell the bird then this normally indicates that parts of it have gone through the core which could damage the ‘less robust’ components or even block the air path or bleed off-takes.
If it was a ‘ding’ on the fan then the chance of damage may be less, but the fan produces the thrust, which is susceptible to minor damage.
I have seen small birds ‘ding’ the fan and bounce out of the intake, generally without any damage at all, but then there is the airframe to think about.
I was unfortunate to have a simultaneous dual seagull strike, one through each engine of a twin jet. Everything appeared normal except the max N2 was only 83% with some vibration. Both engines continued to run, (they were Rolls Royce), but after landing at shutdown they ran down very quickly.