Lots of good info here, and everyone will have a different approach so take mine with a grain of salt. FIRST what I would do is ask myself what the job market for a firefighter position is where you live, and what are the minimal requirements. If there are multiple departments, all actively hiring, and the requirements are on the lower end, then attempting to get hired and starting work right away with the plan to continue on with your education immediately after hire might not be bad. I agree with one of the previous posts in also looking into the possible departments and checking to see if they offer tuition reimbursement. Why pay for school when someone else will, provided you get hired right away.
Being a Paramedic will ALWAYS make you a more attractive candidate for ANY department, as will having a degree, so if there is a way you can get your Paramedic via an associates program, and there are many community college associates programs out there, then I would initially go that route.
As far as the Bachelors degree goes I believe in this day and age everyone should have one. (I do not, but need to get my *** in gear) I think you should first evaluate your goals, and maybe give us some more info before we provide you with that guidance. In this line of work you absolutely need something to fall back on, however depending on your goals might change the advice I would give you.
If you only wanted to be a firefighter/paramedic for a fire department and eventually promote I would most likely direct you towards a management degree, as you will be managing people, stations, maybe later in your career budgets etc. If you wanted a career on the EMS side then the BS in Paramedicine would likely be ok. If you have desire to progress into nursing or flight, or an advance practice route such as PA school or CRNA a BS in Paramedicine would likely be a waste of time that could be spent elsewhere in your educational offerings.
I just precepted someone at my work who actually took a round about way of achieving his goal, however he's young and kicked ***, will be a DNP/CRNA by the time he is 30. He went into a BS Paramedicine program, graduated top of his class and started working as medic. As soon as he graduated enrolled in an accelerated BSN for provider's with an existing BS, and finished his BSN in a year. Took a job as an RN in a muli-trauma ICU, two year's later got a job with us flying regular part time (one shift a week), and just applied to and got accepted to CRNA school.
Moral of the story is there are tons of options, and depending on your level of motivation and goals you can accomplish alot quickly. I WILL tell you I was just like you. Wanted to only work for the fire department and just hammer out Paramedic school. I got my associate's and stopped. Now 11 years later I wish I would have gone the bachelors route. It's hard to jump back into school as an adult learner when you have adult responsibilities, financial ones, and alot of you pre-reqs are expired for anything health field related. So if you can do the BS now, I say go for it. It will never be something you regret/will eventually put you ahead of your colleagues. Good luck!