The lease or rental agreement is probably still in effect. Under that agreement, the landlord or its agents will probably have a right to access for required maintenance and other purposes. The exact circumstances under which they have the right of access will depend on the provisions of the lease or other agreement.
If Alice has a key, she should be able to access the apartment without needing the management to do anything. If Alice does not have a key, she would need the management to provide one. They would quite properly want assurance that Alice is in fact the proper person, and not some other relative or some court-appointed administrator.
Alice could send notice to the management, asking it to limit maintenance access to Bob's apartment to what is urgent and essential, and warning of possible damage to Bob's property. She could send this both by email and by certified mail, as both of these preserve a record of the communication, and keep a copy of the communication with a note of when it was sent. If lawyer for the esatate has been selected, Alice could ask the lawyer to write also, as the managemetn might pay more attention to that.
Meanwhile Alice should attempt to get letters testamentary issued by the probate court as soon as possible. That would give her the legal right of access. This can often be done on a relativity quick basis, depending on the circumstances. It does not need to wait on the full probate process.