There is no guarantee you could get into medicine after doing any other degree, and graduate entry medicine is normally considerably more competitive than standard entry medicine for school leavers. I would recommend if necessary taking a gap year to take any "missing" subjects to meet the requirements for standard entry medicine.
In any case, if you did apply to graduate entry medicine it is an accelerated course but the length is set for graduates of all disciplines (except a couple of courses with dedicated routes for qualified dentists pursuing maxillofacial surgery) that they accept - doing biomedical science wouldn't make it any shorter than if you did physics or anthropology, assuming all are accepted (granted some GEM courses only accept bioscience degrees).
I'd also note that applying to graduate entry medicine is not "transferring" - medical schools do not, in general, accept transfers, with the exception of dedicated existing internal transfer schemes (which are uncommon and even more competitive than GEM - think 200 first year biomedical science students competing for 1-5 places on the first year of the medicine course). The only other transfer arrangements at medical schools are dedicated pathways for preclinical-clinical transfers at St Andrews and Oxford.
I would also not recommend limiting yourself to only a single medical school - chances are not in your favour to start with so you should be applying to four medical schools, and you should choose these based on how likely you are to be accepted ahead of any other consideration. I'd also note that there is no guarantee you could stay in Edinburgh for your entire medical career (and very unlikely you could in fact) since as I understand the Scotland deaneries are pretty large and the one that includes Edinburgh will always have you rotating to other cities/towns outside of Edinburgh as well as Edinburgh itself. You will need to move at some point if medicine is your goal, so you may as well accept that now and apply to other medical schools as well.