The transients observed are due to a combination of using a marginally stable filter coupled with the initial condition matching performed by "filtfilt" to minimize start-up and ending transients, as described in the documentation. This is the reason behind the difference in behavior between using "filter" and using "filtfilt". It is an inherent limitation of the "filtfilt" function.
Regarding the stability of the filter, you may view the filter's stability using "fvtool", (fvtool(bp) in your case). In the Filter Visualization Tool window, select "Analysis > Pole/Zero Plot", and you will see a discrete system pole/zero map If you notice, your zeroes are very close to the edge of the unit circle, indicating the marginally stable behavior of this filter. When this type of filter is combined with the initial condition matching, the numerical conditioning yields the transient results that you observed.