Are modern day bullets magnetic

no they are not

Well... In the sense that many bullets are solid lead, no, they can't be picked up by a magnet. However, many are either steel jacketed (i.e thin outer layer of steel around a lead core), or, in certain cases, are steel cored, these bullets can be picket up by a magnet.

Now, if the question was whether the bullet itself carried a magnetic charge (and, thus, acted like a magnet), the above answer is certainly true: NO, bullets are not magnetic in and of themselves.