I'm not familiar with the term 'bridging course', I am assuming it would be like a 'foundation year' common in the UK, feel free to correct me!
To give you an example, of 4 of my longest standing EE friends, one started with a HND (vocational qualification) and began his career as a service engineer and did his degree later in life, one did a degree through the 'normal' route and then worked as an electrician for many years before working formally as an EE, one started his degree later in life via a foundation year and finally I was thoroughly conventional all the way through. The moral of the story is that these were the guys I shared an office with as a PhD student, we all passed, all now work as well paid consultants, and nobody's background has held them back in any way.
I worked as a teaching assistant whilst I was a PhD student so I spoke to loads of undergrad students who went through foundation years and non-conventional academic backgrounds and I still keep in touch with colleagues who teach courses on foundation years... so that's where my knowledge of the courses comes from..
The foundation years are 'intense' in that there's normally a very diverse range of courses/modules from maths/physics/chemistry topics and a big 'culture shock' for many students suddenly adjusting to university life and the expectation to be much more self sufficient then before... but they have an absolutely massive advantage that they are taught with the knowledge of the degree/further/higher qualification you'll be going on to so the lecturers do tend to put some real applications to the maths which definitely benefits students who are more practically focused and don't enjoy the abstract side of maths. Honestly the students who went through foundation year route were so much better prepared for the first year degree than the 'normal' route students! (I'm certainly including myself in the less prepared, I really began to wish I did a foundation year).
Don't be put off EE because of the maths, yes there is a lot of it, but it doesn't feel so much like maths when you're learning some applications along with the fundamental stuff. I left high school absolutely detesting maths vowing never to have anything to do with it again, 6 years later my 4th year EE module choices included 2 maths-masters level maths modules (and I actually enjoyed them!).