Cut off piece about three inches long at a 45 degree angle
The "bias cut" bowl is a bit of an oddity and only named bias-cut because the blank comes out of a log at an angle rather than having been cut perpendicular to the log. You will see in a moment that when this is mounted on the lathe, there is a point sticking out at one end and the other point sticking out in the other direction. It will look funny and you will find yourself wondering what in the world you are going to do with that!
As I say, this is an odd-shaped bowl and may or may not have a flat or round bottom when you finish it. Using a log about 6" in diameter, cut a piece from the log at a 45-degree angle across the log and about three to four inches thick. The first photo on the left shows two cuts through a five inch log at the best angle with about three inches between them. Experimentation has shown me that the optimum angle is about 45 degrees.
One long point out to each side but balanced
Once this oddly shaped piece is cut from the log, mount the blank on a screw chuck or with a spur drive. Look at the first picture on the right. This is held between centers at first to see how best to utilize the features of this piece. You can see that when you cut an angled piece and then mount it squarely on the lathe, the angles of the bark faces result in a point sticking up at the top and the point from the other face sticking down at the bottom. But the spur drive and live center mounting points are actually balanced, one on one side of the pith and the other on the other side as the pith is now angled on the lathe but parallel to the bark. If the cut sides are positioned so they are as perpendicular to the lathe bed as you can get them, it should work out well. The mounting points should be centered on a line from the long point on each side to the pith on that side. Once mounting configuration is established, I recommend drilling a hole in what will be the top and using a screw drive. Even with a screw drive, always use the tailstock live center whenever possible.
Turned around and held by tenon in chuck
With the weight of this piece evenly configured on the lathe, it will be pretty well balanced until you start cutting away the bottom of the bowl. As you do so, the piece will be more and more out of balance which is actually on purpose and part of the goal for a bias-cut bowl. I don't recommend turning this type of piece on a mini-lathe unless it is mounted on a heavy stable base as the out of balance piece may cause the lathe to move about.
Even off the top and cut out inside of bowl
When deciding how to mount this piece, remember that the side facing the headstock will be the top of the piece, just like a normal bowl. You will first shape the bottom of the piece. It will seem very odd as you will be initially cutting wood only for a short distance per revolution as much of it will be just air until you cut further in toward the center. Remember, you are cutting off that long point where you are making the bottom of the piece. For the first one, cut straight in from the outside toward the live center. Flatten the bottom up to the live center and then repeat, cutting in only as far as where you will be making the outside of the bowl part. You will also need to cut a tenon on the bottom to be gripped by your chuck when you turn it around. See the second picture on the left. Whenever making any bowl, it is always fun to try to utilize any features of the wood to best advantage, such as knots or even a small branch sticking out. Shape the outside of the bowl section up toward the bottom of the top flange. With a 6" piece, leave the top about 3/4" thick for now. You can trim it down to about a half inch from the top once it is in the chuck.
Once the piece has been reversed and the tenon held firmly in your chuck, you can face off the top. The tool rest should be placed perpendicular to the lathe bed and close to the top part of the piece. It may be easier if you remove the tailstock completely from the lathe. With a 6" log, don't cut that top flange any thinner than a half inch for roughing it out. Once cut flat and to desired thickness, turn (so to speak) your attention to the inside of the bowl. Hollow out the inside just as you would on a standard bowl. If doing a roughed out piece, leave the bowl about a half inch thick from inside to outside, remove from the chuck, and Anchorseal it before placing aside to dry for several weeks.
Once dry, or if continuing with the green wood piece, jam chuck the piece over a 4-jaw chuck with the jaws up inside the bowl and the tailstock holding the piece in place. Make fine cuts on the outside and sand. Be cautious sanding the underside of the flange as that will be wood, then air, then wood, then air, and so forth. With care, it can be sanded with the lathe running. Don't get your hand in the arc of the spinning flange.
Turn the piece around and grip it with the chuck. Complete the flange by reflattening it and then cutting it to final thickness. Further hollow out the inside of the bowl so the thickness of the sides match the thickness of the flange. Sand the inside of the bowl, and with great care, the face of the flange. The flange may be easily sanded with the lathe off at this point.
Take the piece out of the chuck and set it on a table using the tenon as a foot. If it stands, you can consider turning that tenon into the base of the piece. If it falls over, then round off the tenon to make a round bottom. Do that by jam-chucking the piece with the tenon toward the tailstock. Cut away as much of the tenon as you can while still leaving a small column of wood between the live center and the bottom of the piece. Sand the bottom and then remove from the lathe, cut off that column close to the bottom of the bowl and hand-sand the nub down to smooth.
This piece is really meant to sit on the bottom of the bowl with the long edge also down on the table. It is too small to be of too much practical value although could be used for earrings or other small items. It could be used on a coffee or end table with a few M&Ms in it, too, and would be quite a conversation piece, usually starting with something like, "How did you make this?"