Here's my $0.02.
While a BGL is necessary, the next of kin/responsible party is irrelevant. The pt is 18, which means she has to make the decision for herself.
That being said, I'm not necessarily concerned about the elevated pulse & respiration rates. She was just biking, of course she's going to be elevated. Along that thought process, chances are she may also be an avid cyclist/athlete, which means she may have a low BP normally. Now, while the lack of memory for the event as well as date/time is concerning, we cycle (see what I did there? ) back to the necessity for a BGL.
Now for the heart of the matter: Do we allow this pt to refuse tx & xport? This is where you need to do a really good focused H&P on the pt. Find out if those vitals are normal, if she has any known medical issues, etc. After performing that H&P, if everything checks out..we can start down the refusal pathway, whereas if there are issues found, things would need to take a different turn. If after everything we do & find, she still wants to refuse, it is still ultimately her decision. So here's what we do: explain the risks of refusal (possibility of unseen/UNK injuries & explain that the possibility that there is a chance those injuries could lead to more serious events [to coin the phrase: SZ, coma, death]). My next move would be to explain that I work under a MD's license, & I would need to contact him/her to explain the situation, & that I would express to that MD the pt's wishes to refuse tx & xport. If my MD is ok with the pt refusing, then by all means she can, but if not - I would need to xport the pt.
Given the above, if the pt is allowed to refuse: I would explain that refusing right now does NOT mean that tx &/or xport can't be sought later. I would HIGHLY encourage the pt to seek further medical tx on her own, or contact EMS if her S/Sx change or worsen. One thing I would explain to the pt is that at the moment, she still has a lot of adrenaline pumping through her system due to the events & that once that adrenaline wears off, she's likely to experience increased pn or other S/Sx, which would then be an indication of the need for further medical tx. After that point, I would ensure that the pt signs my refusal form, as well as grab a witness (non-family, non-EMS) signature if possible.
So what do we take away from this? The bigger question in this scenario is: What caused the pt to crash on her bike? Was it an underlying problem such as a low BGL, or did the memory lapse come after the event? The biggest assistance we can provide as EMS professionals is not getting sidetracked by surface level problems; we MUST dig deep, think critically, & be all inclusive in our exams & tx's.