Tulip garden is 18kms away from Srinagar airport, and 8kms away from Lal chowk city Center. There are bus services, which operate till Boulevard road, and from the stop you have to walk to the garden. Another way is taxi and cab services that are available. Will share a few tripoto links, written by travellers pertaining to their travel to tulip festival Kashmir, see if it is suitable for your travel. Regarding travelling solo to Kashmir, from what I hear from people I know is it is safe to travel solo. Here are some tips for solo women travellers written by tripoto travellers, just in case it might be useful for your travel.