How do I create a bleed for an irregular shaped vector?

It is most certainly a "normal thing to do" and from the sound of your description of the project, you definitely need to do it.

Creating bleeds for die cut (or plotter cutting) is, in principle, the same thing as building bleeds for rectangular trims: your artwork has to extend beyond the cut by an amount greater than the accuracy variance in the cutting.

Just as you would build bleed for each differently-colored object that contacts an ordinary stright trim, you do the same for  each differently-colored object that contacts the die-cut or knife cut. The most expedient way to "extend" an object for a bleed depends on the object. It may be simplest to do it using an offset path command. (I usually don't; offset path offsets all the way around the whole path; it has no idea which parts of a path are on the page and which parts contact the trim.) It may be simplest to just move a few anchorpoints.

I don't know why anyone is complicating a question about basic bleeds with the issue of trapping. Trapping is a separate issue, and may not even apply, depending on how the item will be printed, which you have not stated. You say the artwork will be printed on white vinyl. Nowadays, that typically means it will be printed by a composite color device (vinyl printer/plotter), not by an offset printing press or silkscreen. Trapping is only a problem when component colors are separated and printed by individual "hits" on the printing device.

JET