Polyester does not bleed in the wash like other fabrics do.
However it's still recommended to keep the colors separate because other fabrics could bleed their colors onto the polyester fabric.
When washing polyester it's best to wash the polyester by itself with other polyester and not throw other clothing or laundry in with it.
It's possible for polyester to bleed in rare cases but polyester doesn't bleed in the wash like other types of fabrics.
Polyester can shrink but Polyester does not shrink as easy as other fabrics.
Since Polyester is a man made Polymer and that makes the fibers synthetic and prevents them from shrinking so easily.
If you have the heat on high enough in a dryer then it could be possible for the Polyester to shrink but it takes some effort to get Polyester to shrink unlike some other fabric.
Also polyester can melt in the dryer when you have the dryer on the high heat setting.
If you need to dry polyester it's best to either hang the polyester out on a clothesline to dry or place the polyester in the dryer on the cool setting.
Having the dryer on the high heat setting when you're drying the polyester will cause it to melt easily.
So just make sure if you do dry the polyester in the dryer that you have the dryer set on the cool setting to avoid melting the polyester.
I have melted some polyester before in the dryer because I had the dryer on the high heat setting and forgot to change the setting.
Now I just try to dry the polyester out on a clothesline to avoid possibly melting it.