As you have a B permit you gain certain "privileges" this means that you have more freedom to move around but technically you are still tied to your employer and the issuing authority (Kanton). HOWEVER, unlike an L-permit, unless there are extenuating circumstances such as a criminal record you will have your permit renewed easily. Your Aufenthaltsbewilligung is not the same as your Arbeitsbewilligung. You need the first to get the second and usually you'll need aproval for the second to get the first (confused yet??

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Once you receive a job offer your new employer simply must inform the authorities that you are now working for them. Really the paperwork lies on their side not yours. It goes a bit like this:
You resign
Current employer informs authorities
You sign new contract
New Employer sends copy of contract in to authorities
Everyone happy ...
HOWEVER, I am a Swiss national, have never had to deal with this other than for employees... so PLEASE do not take what I say to be the 100% truth.