Bulb Energy Claims:-
Every year, the average Bulb member saves 3.5 tonnes of CO2 from entering the atmosphere. That's like planting 1,770 trees.
They also state:-
We buy our energy from independent renewable generators from across the UK, like Gail and Miles from Old Walls Hydro in Dartmoor. Wherever possible, we have direct relationships with these generators to purchase their electricity. We buy the rest from the wholesale market. We source our energy from solar, wind and hydro. They're a pretty impressive bunch, our generators.

My observation on the claim from bulb is as follows:-
Since Bulb buys in the renewable electricity from existing sources the act of a customer purchasing from bulb does not save carbon. The carbon is being saved whether a customer buys electricity from bulb or not.
Government guidelines on Company greenhouse gas reporting state that companies purchasing renewable electricity cannot claim it as zero carbon( Appendix G , p49 of https://assets.publishing.service.gov.uk/government/uploads/system/uploads/attachment_data/file/69282/pb13309-ghg-guidance-0909011.pdf)
The reason for this guidance is that green electricity sources have grid priority which means that all green electricity available is always consumed. It can be consumed by customers choosing to buy green or if they do not so choose, it is consumed/ shared out by all consumers. The carbon reduction is the same in either case so Bulb should not claim that buying energy from them prevents release of 3.5tons of CO2.
The danger in this claim is that customers believe that their use of electricity has no environmental downside and they therefore need not reduce consumption. This belief is false because demand which is not met by renewables is made up by burning gas. If customers on green tariffs reduced their consumption, this would release more low carbon electricity to be shared among the remainder and less gas would be burned.

Update 2019-10-16