say hi...
dont make it more complicated...
you dont have to learn everything about her all at once...
try not to make any expectations...
just be friendly - say hi and bye - if a conversation sparks... then thats great, after you say hi a time or 2 maybe you will feel more comfortable going further...
just try to be natural and dont force things... keep it simple - i would say...

you can do it... if nothing else maybe you will just make a new friend to work out with, that may be just as cool right..? give yourself that extra push next time you see her to just simply say hi .. if that comes out good, maybe can start a conversation just by saying you seen her there a few times and didnt want to seem rude by not saying hi

dunno, im not that great with relationships...

good luck... you never know - maybe she is thinking the same thing...
god knows i would probably do the same thing as you - but im getting older and i know that its better to find out rather than wonder the rest of your life...