Cheapest way: Beijing to Chengdu by train, but it will be a long jorney
Cheaper way: fly to Chengdu from Beijing and take 10 hours bus to Jiuzhigou
The most expensive way: Fly to Jiuzhaigou airport from Beijing
No problem for you travel alone, perhaps the last way is the most convenient and safe as you said. However the flight ticket is expensive. As the data shows, it is over 2000RMB now.