I have been carrying my BOM in a zipper bag I got with a set of curtains. I slip my scissors and marking pen in the pocket that held the lable, then put in my spools of thread (sometimes I use bobbins instead) a needle case with all the sizes I might need, a thimble, a small pin cushion, precut peices and of course the block.
When I am hand peicing my Civil War blocks I use a block caddy I made from a peice of felt backed with a fat quarter - I fold it in thirds lengthwise, then in half so it forms its own little purse shape. I added handles and a button closure. I use safety pins to pin my block peices inside and secure a couple of needles before i fold it then once it is folded I slip in my thread and thread snips. All self contained.
Another project my dd found to be very portable was making yo-yos with the clover yo-yo maker. All she needed was a bag of scraps, the yo-yo maker, her scissors, needle, and thread. She made yo-yos in the back seat of the car all the way from WV to Lancaster PA.