Poor baby!

So glad she's found you, and you've found us!
Here is Bouncing 101 for you
Bouncing is a phenomenon that occurs when the body experiences (or at least thinks it does) hypoglycemia. Luckily the body uses bouncing as a defense mechanism against this where it attempts to compensate the low blood sugar by dumping excess glucose provided by the liver in an attempt to raise blood sugar back to “normal” numbers. Unfortunately, “normal” is a relative term according to the body. For a diabetic whose body has been untreated for so long that it considered very high numbers to be the new normal, lower numbers can often make the body overreact in attempt to save itself, even if it’s not in danger.
A cat who has been suffering from diabetes for some time may at the point of diagnosis have a new “normal” of 400. When insulin is introduced and brings it down, even to 200 (still diabetic levels), the body thinks it is in danger, dumps excess glucose, and thus the blood sugar skyrockets up to the 400-600s. After enough time has passed, the body will eventually realize that 200 isn’t such a bad number, and bouncing will happen less often. Note some cats are extremely bounce-prone and a switch to Lantus/Levemir is needed.
There are three main causes of bouncing: when blood sugar drops too low (hypoglycemia), drops lower than the body is used too, or by dropping too much too quickly. Typically if a cat drops more than 50% of their blood sugar a bounce is likely to happen, or if they drop 100 points within an hour.
While bouncing can be considered as a safety net in the instances of hypoglycemia, it can look very confusing on paper.
That said, Bitsy's numbers are in no way unusual for a new diabetic. For one, Bitsy sounds like she's been poorly for quite some time and so these high numbers she's having are her new "normal" - as stated above. It will take some time for her numbers to go down, just don't rush it ... like your vet is trying to do. It's very possible (and likely) that Bitsy is dropping from the insulin and her body is reacting to the lowered glucose by spilling more glucose in (again as stated above). If you don't "catch" the lower numbers, it just looks like a bunch of high 400-500s.
There's a lot to take in and learn but let's stick with the basics right now:
- Test before giving insulin every time - you never know when they're too low for insulin! Right now too low is anything below 200.
- Mid-cycle tests are important for seeing how low the amount of insulin you're giving is taking Bitsy. On Prozinc getting tests between 2 and 7 hours after insulin is most helpful.
- Remember that bouncing - those high numbers - can take up to 3 days to clear the system. Don't get discouraged by them, it's normal!
- Small meals throughout the day - a good guideline would be to give a snack 2, 4, and 6 hours after giving insulin. Once we find out how Bitsy reacts to the insulin, we can adjust this later if needed.
- Reduce the dose by .25 units if Bitsy drops below 90 at any time.
- New diabetics need twice as much food as a regular cat. If Bitsy is underweight, give her even more if she wants it. The hunger will wane once she's better regulated.
- Feed at night!! Get an autofeeder (Petsafe 5 is popular). Cats drop lower at night. For all we know she's dropping late in the night and then all we're seeing are those high numbers in the morning.
- We are always here to help.

1 unit is a good starting dose. Bitsy does not "earn" an increase until one week has passed and her numbers INDICATE the dose isn't going low enough. Ideally we want her nadirs (lowest point in the cycle, usually around 5-7 hours after Prozinc insulin) to be below 150. You are correct to think that jumping to 2u is too much. Some vets think cats are dogs!
If you can (schedule permitting) start getting in tests during the day (+2, +4, +6 one day, +1, +3, +5, +7 another - rough example, doesn't have to be exact) we can see once the bouncing clears how well the dose is doing for Bitsy.