The best time to visit Bikaner is winters that are November to February. In winters the climate is mild and best for sightseeing and travelling. You can also visit Bikaner in summers if want to get roasted in the sun. Else every season is good enough to see different colours of Bikaner.
You can reach Bikaner as per your comfort level like if you are comfortable with the plane, or with train, or by the road, it all depends on your personal choice. Every route has its own experience.
PLANE- there are no airport in Bikaner particularly, the nearest airport to Bikaner is Jodhpur and from there you can hire a taxi service to reach Bikaner.
TRAIN- Bikaner is connected to other major cities in India through railways, and has 2 railway heads. You can easily find trains to Bikaner, from railway station you can hire a taxi to go your hotel or to the places you want to visit.
BY ROAD- if you want to experience different things from inside, it is the way best for your journey. By road you can get public bus heading towards Bikaner. The condition of the road is good and the route is safe. In case if you hire a private cab to the destination.