'Since' is used with 'ever' as an adverb. The proper way should be 'ever since'.
The correct sentence should be: I met her about ten years ago and have remembered her
is used in different ways- (i) as an adverb of time (ii) conjunction of time (iii) preposition of time.
As an adverb, it has two meanings.
|1) From then (i.e. from some time in the past up to now) ||e.g. I met her about five years ago and have remembered her ever since.|
|2) At or during some time between then and now||e.g. He told me last month and has spoken of it several times since.|