Any savings for "bundling" would be via EE One which you can read about here: https://ee.co.uk/ee-one
Is your BB with EE currently and is it within the minimum contract term or out of contract?
That SIM deal is cheaper than any offered even with maximum discount, especially Unlimited Data. The EE One Unlimited SIMs now start at £11.50pm after the latest price change, so you've got a great deal there.
The financial benefits would likely be negligible in your case, unless your BB is out of contract - in which case you could potentially get EE's Full Fibre 150 for £29.99.
It sounds like that's the plan you originally had and it increased by the standard yearly £3 for Broadband on the 31st March, so likely nothing you can do to drop anything down until you're out of contract and see what prices are like then.
