Are there any bugs or ways to make my divisor code better?
Here are some thoughts on this code:

Chose descriptive function names

The name programme is not really very descriptive of what the function does.  You might call it something like factor to give the reader of your code a better idea of what it actually does.

Document your code

Python supports the use of multiple different kinds of comments, including ones that can be made into unit tests.  Get in the habit of commenting your code carefully.

Separate I/O from calculation

The main purpose of the program is to factor numbers into divisors which is something that is potentially reusable.  Both to make it more clear as to what the program is doing and to allow for future re-use, I'd suggest extracting the factoring part into a separate function and the have the input from the user be done within the main routine or some other input-only function.

Separate timing from the thing being timed

On my machine, the timer always reports 0.0 seconds, which makes it hard to compare the effects of changes in the code.  For that reason, what's often done is to call the routine to be timed multiple times to get better resolution.  In order to do that, you'd have to remove the timing from the routine you're timing, which is good design practice anyway.  Right now, the print function is part of the code that's being timed.

Think of your user

Right now, the user has to enter "yes" or the equivalent and then enter another number to be factored.  However, the prompt doesn't suggest that "y" is a valid answer.  Adding that to the prompt would help the user understand what the computer is expecting.  Better still, would be t eliminate that question and to simply ask for the next number with a number '0' being the user's way to specify no more numbers.  Of course the prompt should be changed to tell the user of this fact.

Expand the range

Right now, the size of numbers that can be factored is limited to what will fit within an int, but it would be much more interesting to be able to factor really large numbers.

Use divmod() to save some time

Right now, for every successfully discovered divisor, the program performs three division operations:  one for %, and then two more to insert the number into numbers and again to print.  Instead, you could do the division once using the divmod function which gives you both the quotient and remainder at the same time.