This is indeed a somewhat awkward use of Bestellung.
Bestellung usually means
1) The act of ordering something
2) The list of things that were ordered
However, in the sentence
Ihre Bestellung mit 50 Mausefallen wurde versandt.
neither of the two applies. The author of that sentence obviously uses Bestellung in a third way, namely
3) Contents of the shipment / the things themselves that were ordered
This is a metonymical use of Bestellung: the word is used not for what it is originally intended, but to name a thing somehow closely related to that original meaning. In the concrete case, there is a leap from "the list of things" to "the things themselves". This is of in principle legitimate, especially in poetry. Also between Meaning (1) and (2) there is a metonymical relationship: from "act of ordering" to "the list of things ordered".
I suppose that this is rather a result of lazyness or sloppyness on the side of the people working for those delivery services, not an effect of their love for rhetoric figures (or knowledge of them).
Now, if you accept the use of Bestellung with meaning (3) as "the items that were ordered", then the use of mit seems more or less an acceptable solution. I would not know what preposition to use instead.
? Ihre Bestellung von 50 Mausefallen wurde versandt.
? Ihre Bestellung über 50 Mausefallen wurde versandt.
? Ihre Bestellung auf 50 Mausefallen wurde versandt.
All these are a bit awkward, although not completely impossible.
A stylistically clean way to say it would be:
Sie haben bei uns 50 Mausefallen bestellt. Wir haben die Bestellung bearbeitet, und das Paket ist jetzt unterwegs zu Ihnen.
This avoids unusual metonymies (Bestellung is used here in Meaning 2, which is a metonymy, but I think this is so established usage that it does not hurt anymore), and verbs refer to subjects that totally fit the standard: a parcel can be on the way, an order can be executed.