How and should I ask her out?

She is my friend from last year. She is very studious and very moody type of female sumtimes her talks r very responsive n sumtimes she completely avoids. We meet online but she never starts the chat and once dnt knw wat hapnd she started flirting and she was like "r u single , or is der any lucky gal whoz dating a handsome lik u" ..den again sumdays later she avoided. Now shud I ask her out?..Well she also took my red rose on college rose day and took a photo wid me. So how shud I ask her out as v rarely chat on net and her mood is always swinging and also gets angry easily. And one more thing 10mnths earlier I went on a date wid her best friend. please suggest how to ask her n also where ...muvi? cafe? or wat?...thank you cheers!!