@Topseyt
Don't take it so personally. Perhaps she is like me and hardly ever active on there. On the odd occasion I do look in on it I find friend requests and suggestions from people I have hardly ever come across.
I guess the point is though, that this colleague has not been 'inactive,' she has actively declined the friend request, which is not quite the same as just 'not accepting' it. She has seen the request, and has gone in and clicked 'decline friend request...'
The OP can tell that because when she sent the friend request, the 'send friend request' button would have changed to 'friend request sent.' Then once the other person accepts, the button changes to the word 'friends.'
However, the button has shown up as 'send friend request' once again, which shows the friend request has been denied and rejected.
Rightly or wrongly, I think it's acceptable for the OP to be a little bit miffed. She thought she had a connection with the colleague, and she has basically refused her friend request. (Although the OP's colleague has done no wrong in doing this...)
I would send the friend request again, and if it's declined again, just let it go and assume she doesn't want you on her Facebook friends list. That is her right, and I wouldn't behave any differently towards her. Maybe as the friendship progresses, she will add you @moutonfou
For now though, don't stress about it. Everyone is different, and whilst some people will add a monkey they met at the zoo, some people are a lot more choosy and picky, about who they have on their facebook friends list.