Honestly, I don't see any obvious reason why a novel cipher design couldn't be the subject of a bachelor's thesis. And presenting it as part of a thesis could even be a decent way to get others to look at it and maybe analyze it.
Admittedly, a more conventional choice for a bachelor's thesis might be something like a basic cryptanalysis of an existing cipher (or, more likely, a weakened version of one), or even just a literature review on the design of a specific cipher and any published cryptanalysis of it. Such a thesis might be easier to grade, as it's relatively straightforward for an examiner familiar with the subject to verify that your cryptanalysis works, or that your description of the cipher and its history is correct and omits no relevant references.
The point is that a bachelor's thesis is not, in general, expected to necessarily contain any novel and original research, but merely to demonstrate the candidate's familiarity with the subject and/or their competence in applying standard tools of the trade. While presenting original research in a bachelor's thesis is generally not forbidden, your advisor might be legitimately concerned that a thesis that tries to stray too far from the beaten path might be difficult to grade, difficult to advise for, potentially difficult to complete if your run into unexpected problems, and at worst might end up lacking in the aspects that a bachelor's thesis is supposed to demonstrate.
All that said, if you really want to do your thesis on a novel cipher, you might be able to sell it to your advisor as an exercise in applying established cipher design and analysis techniques. If you choose to follow this path, I'd recommend keeping the following things in mind:
Treat your design as a "toy cipher", something constructed and analyzed for the sake of practice.
The odds are that your first cipher won't withstand serious cryptanalysis — and even if, by some miracle, it does, you'll almost surely later think of ways to improve its performance, versatility, footprint, etc. If you're lucky, you might come up with some neat ideas that could be reused (by you, or by others citing your work) in later designs, but you shouldn't expect your first attempt to be any good except as a learning exercise.
Don't stray too far off the beaten path. You're supposed to be demonstrating that you know the standard tools of modern cipher design and how to apply them cleanly, so make sure to actually do that.
Whenever possible, try to borrow standard, already well analyzed parts (S-boxes, etc.) from well known ciphers — the more standard components you use, the easier you make it for your advisor and readers to see how well you're putting those components together.
If you really want, you can include one neat new idea in your otherwise conventional design — but if you do that, be prepared to spend the greater part of your thesis (and at least 90% of the effort in writing it) on clearly explaining, formalizing, justifying (e.g. by showing its mathematical equivalence to a more standard design) and analyzing that one novel piece.
Analyze your cipher. This is important. The world is full of home-grown hobbyist ciphers presented without any attempt at cryptanalysis, and they're all basically worthless — you don't want to contribute to that pile of junk.
Ideally, at least half of your thesis, and preferably more, should be about cryptanalysis of your cipher. Even so, you may not have much room (or time) to carry out an extensive cryptanalysis in a bachelor's thesis, but you should present at least one basic cryptanalytic attack on your cipher, just to demonstrate that you know how to do it.
BTW, it's perfectly OK if you end up breaking your own cipher — that's why I said you should consider it a learning exercise to begin with. In fact, if you can't break your cipher as originally presented, I'd suggest at least breaking a weakened version of it. Don't forget to include an invitation for others to continue the analysis where you left off — who knows, someone else might find it an interesting challenge.
Have a backup plan to scale down your thesis, in case you still find that your original plan was too ambitious. You can always save the extra stuff you cut out for later publications, or perhaps for your master's (or Ph.D.) thesis.
Discuss this with your advisor — it's very important that they know that you're not going to get stuck just because you've bitten off more than you can swallow, especially as they seem already worried that this might be the case. You should also talk with your advisor to ensure that, even if your initial thesis plan is a bit unconventional and ambitious, at least your backup plan involves things that are squarely within their own area of competence, and which they therefore can effectively advise you with.
Finally, keep it simple! A typical bachelor's thesis is about the size of a single journal article, and much of it will typically consist of summaries of background material. There's really not a lot of room for anything fancy or ambitious there, so trim things down as much as you can. The odds are, whatever you think is as simple and basic as it gets is still far too complex. Again, remember that you can always save the fancier stuff for later publications and theses.
Of course, the length and scope of a bachelor's thesis can vary a lot between fields, countries and individual institutions. Your own university may have guides on what such a thesis should contain and how it should be structured, and your advisor should certainly be able to provide you with examples of what kind of work they expect from you. Still, remember that a bachelor's thesis is basically the first tentative step in your academic research career, not your magnum opus. It's really more like just a glorified final essay or class project.
Mind you, I'm pretty sure I've never met anybody, myself included, who picked their own thesis topic (as opposed to just having it handed out to them) and wasn't at least a little bit too ambitious about it. The best survival trick I've found is to notice when you're running out of time, space or effort, and just ask yourself (and maybe your advisor) "Do I really need to make it so fancy?" Usually, the answer is "No."