I asked a similar question a few weeks back. I ended up using the following function, which I called after making changes to the tab title and appearance. Seems to mostly work, even when adding characters or adding/removing bold stuff. I'm sure there is some optimizations (handling the Bold being Default instead of True).

        private void ResizeTabWidth(UltraTab tab)
        {
            // This assumes that tab.Appearance is set up before this is called.
            
            // Figure out which font we're using.
            FontStyle fontStyle = tab.Appearance.FontData.Bold == DefaultableBoolean.True
                ? FontStyle.Bold
                : FontStyle.Regular;
            float fontSize = 8;
            Font font = new Font("Arial", fontSize, fontStyle);
            string text = tab.Text;
            bool canClose = tab.AllowClosing == DefaultableBoolean.True;

            // Recalculate the new width of the tabs. If there is a close button (canClose is true), then we need to
            // add space for that.
            Graphics graphics = CreateGraphics();
            graphics.PageUnit = GraphicsUnit.Pixel;

            SizeF textSize = graphics.MeasureString(text, font);
            int decorationWidth = 12;

            if (canClose)
            {
                decorationWidth += 15;
            }

            // Set the fixed width of the tab.
            tab.FixedWidth = (int)Math.Ceiling(textSize.Width) + decorationWidth;
        }