I'm sorry to tell you that, but your approach is wrong. That's not how you train separation and independence with your dog.
What you currently do is training a command. You say a specific word, your dog does what is expected of her and she gets a reward. There is a clearly defined beginning (the word) and a clearly defined ending (getting a reward). Most dogs have an attention span of a few seconds, so prolonging a command over several minutes is extremely difficult for them.
What you want to do is establishing a behavior. There might be a defined beginning (like saying "god bye"), but there is no clearly defined ending, at least not withing the attention span of a dog. You basically want your dog not to do things like whining and barking during a long period of time.
The way you conduct your training right now, you basically want the dog to "hold" the command for a prolonged time and wait for you to be released from the command. What would happen when the training progresses to one hour? Two hours? You'd train your dog to stay motionless on her bed and waiting for your return. That's not independence. It can actually cause separation anxiety because you gave your dog a command and she need you to release her from the command again.
To properly train separation, you should not use the command "stay". You can establish a different word to signal the start of the training, but you need to clearly separate the words used for commands from those used for behavior.
You can start the training the same way you did until now. Bring her to her bed and say the the new command. She doesn't have to sit or lay down. Leave the room and observer her behavior in a way that she doesn't see or hear you.
Acceptable behavior includes:
- sitting or laying on the bed - that's a relaxed pose;
- walking around the room, sniffing around, interacting with toys or chewing bones - that's independent behavior.
Behavior that indicates she failed the lesson includes:
- sitting right in front of the door for more than 3 minutes, scratching or biting the door - That indicates separation anxiety. She anxiously awaits your return and refuses to relax or occupy herself with anything else.
- howling or barking for longer than 10 seconds after the initial seperation - This is typical problematic behavior that causes a lot of problems with the neighbors and landlords.
If she fails the lesson from the very beginning (less than 3 minutes), keep the lessons very short and help her by distracting her with a chewing stick, a food dispenser ball or a snuffle mat. If she needs 1 minute to eat her treat, let her wait an additional 30 seconds at first before gradually prolonging the waiting time.
If she manages a longer time, observe her behavior during the seperation. If you notice that her behavior gets more and more unacceptable (she spends more time in front of the door, she starts whining after having been quiet a few minutes), stop the lesson at that point, return and reward her with your voice and treats. You always want to make her succeed (because that produces the best learning results), so stop the lesson before she fails. If she (almost) failed, return to a shorter interval that you're sure she can manage for the next lesson.
There is no set regimen or algorithm to determine the length of each lesson. Some dogs are very independent and are happy with the company of a toy or a chewing bone, other are very attached and need longer to learn that separation doesn't mean abandonment.
You'll get the best results if you stop each lesson before your dog fails and adopts anxious behavior. That way you build an experience of "You don't need to become anxious because I'll always return."