most hotels are busy enough that it doesn't make a difference if one has a key-card on entry or not (someone will always be using a lift and a couple mins wait is no issue)
you can always phone up and see
just ensure you book her during a busy period and not at a time like 10pm onwards when its a ghost town inside.
personally "call" the girl and speak to her. within 30s she will understand if you are genuine and understand your hesitance or insecurity.
as for discreetness
1-use sites like booking.com or expedia. more often than not you can fake the address and name as long as the credit card number is legit the booking will still be fine.
2- use the same name twice. john john. tim tim. etc
3- while some girls will call - most wont even bother but do expect some extra towels or the sort delivered to the room as an indication a check has been carried out.
4- use a 3-4* hotel and you will usually have no reluctance from the girl.
5- if your still worried then book an apartment. While these are similar to hotels and usually around the same rate - it could be more beneficial to you.
most hotels dont ask for id. 9/10 will only ask for a signature if its a booking made externally ie booking, expedia, laterooms etc. its not hard to "get a friend" a hotel so any name will do - just rememebr it and have a print out of the booking ref.
they will ask for a signature more than the address. same city fake address would easily work.