Is AS Further Maths enough for university-level Mathematics?

I've just recently finished my A Levels and took Maths, Physics, Chemistry and AS Level Further Maths. I only took AS FM because I realised too late that I would need it for uni and so studied it by myself (without any school assistance) in Year 13. I've covered a small amount of the Year 13 FM content (Basically Polar Coordinates and Hyperbolic Functions) on top of the AS content, but will that be enough?
And also as a side note, since I taught myself the content, is it worth calling up the unis to ask for a reduced offer? My maths teacher told me I would likely receive a reduced offer because of it but had to fight on calls for a place at Bath when they have they already have offers that include AS FM so I don't see why I had to fight for it instead of being offered it straight away.

No, don't call for a reduced offer - it's a waste of time. You are fortunate they've even offered you a place and it was your choice to study FMaths by yourself - you could have joined a class at school.

My school didn't offer further maths as a subject, which is why I had to teach it to myself in the first place.

I am, if I remember correctly only 3 students in my year signed up for it and they said something about being too understaffed to run actual courses for it I think, I was only told way later on in the year that I'd need it for uni (hadn't even crossed my mind) so I learned the AS over summer and Year 13 by myself since they still didn't run classes

Well you don't "need it for uni" - there are only a few UK unis that require FM, so you still have plenty of choices

I am, if I remember correctly only 3 students in my year signed up for it and they said something about being too understaffed to run actual courses for it I think, I was only told way later on in the year that I'd need it for uni (hadn't even crossed my mind) so I learned the AS over summer and Year 13 by myself since they still didn't run classes

a few years ago there seemed to be much fewer, (Cambridge didn't used to, on paper, until a few years ago) but a pretty good proportion of the top UK universities for maths now seem to require further maths. Bath, which the OP has listed, now wants people to do at least AS FM as a rule. (I swear when I applied nearly 5 years ago they did not require FM at all, I think UCL didn't either but they do now)

Though OP is in a better position than many because their school couldn't offer FM, it still seems to make it much harder to get in to top universities that usually require FM (Oxford, Imperial, etc.). Whether this is because people without FM tend to be weaker mathematically (and so don't give a good showing on the MAT/TMUA/etc.) or because it casts serious doubt on their application would be another question.

All schools in England can offer FMaths through AMSP - it's taught online

https://amsp.org.uk/

"The programme provides national support for teachers and students in state-funded schools and colleges in England. Additional, targeted support is offered in areas of low social mobility and low participation in Level 3 maths with the aim of increasing opportunities for all students to study maths post-16, regardless of their location, gender, ethnicity, or background."

would point out that universities still have allowances for people who "can't take FM" or "whose school doesn't offer FM" (more or less their wording) so I don't think AMSP is viewed by them as a definitive solution.

They could though through AMSP - they just didn't bother

It won't apply in England though because ALL state school have that option.

i think this would have been stipulated by the university if it were the case, but I think not offering FM as a "normal subject" would be sufficient to those unis for those purposes.

I don't really know enough about the AMSP to comment whether this is the correct approach from them and whether they should just ask applicants to use it.