If you've asked her out previously and 'nothing has come of it' then I am dubious as to whether she would even appreaciate your valentines day advances. Shy or not, it oes seem rather odd that you've often asked her out and nothing has ever happened.
If you still insist on sending her a card then put it through the door and leave flowers in a vase also at the door, (you can ring the bell and then walk away) as it all sounds rather full on to me for someone you're not actually seeing and I'd personally feel pressurised if some bloke was stood at my door with a bunch of flowers on valentines day.
Finally, ask her out again by all means but actually set a date and a time to meet and if you can't/don't/she seems vague then that 's it, don't ask again as it really doesn't sound like she's that bothered. Sorry, but that's how the situation looks to me, hopefully I've read it wrong but as it sounds, doesn't look promising.