"I do not want her to wait for me."
Translation:Benim için beklemesini istemiyorum.
to wait for someone = birisini beklemek. i guess it would be a better translation here.
birisi için beklemek especially means to wait because of / for the sake of someone. but when these meanings overlap (as in this example) you can also use birisi için beklemek to mean to wait for someone, it sounds okay.
if your waiting is not physical you can only use birisini beklemek.
I am waiting for the new iPhone. -> Yeni iPhone'u bekliyorum. (Yeni iPhone için bekliyorum would sound as if you were waiting in line in front of an Apple Store)
The real suffix is -i: the accusative case suffix showing the direct object of the verb istemek "want".
The -n- is a buffer consonant because Turkish does not like two have two vowels next to each other.
bekleme = waiting (as a noun: the act of waiting)
beklemesi = her waiting
beklemesini = her waiting (acc.)
I do not want her waiting = I do not want her to wait.