I think it would take 50,000 years.
Nope...you can do it in under 50 years. If you accelerate at 0.1g the whole trip (half would be acceleration, half deceleration) the trip takes about 10 years, at 5 years for signal reception and you’ve got a minimum of 15 years. Lower accelerations give you longer trip times. I have a chart in a book somewhere.