How come you talk until like you have fallen for her. 
You get rejected being friends? I never kena b4
leh...... Lols..... and also, you are afraid of rejection by her,
and you fear her give you single word answers. You are sort of
despo in wanting to be friends with her..... Quite obvious u like
her........ 
Also, even if you are down right ugly, you can still be friends
with her. Looks are not the key issue, unless you talking about r/s
larh, obviously u want her to be your GF right? Scared you ugly she
reject you, you like her izzit?
As what others said, be confident. Try this, "Hello, you looked
familiar. Have i seen you before?" If she say, " erh sorry leh,
think you got the wrong person.", give her a smile and say "pai seh
pai seh! I got the wrong person liao! Sorry arh!" Try this method
if she's friendly, if she's not, NOT RECOMMENDED to do so.
Last time i got the wrong guy(its a guy ), and he just smiled and
laughed at me. Then we talk awhile just like that. Try to start a
conversation with her first. 
Good luck!
