Try something like this: It checks every time a user presses a key if it checks if it exceeds the textbox and if so if focusses the next one. Not sure if this code will work 100% on ASP.NET but I think it should give atleast a good idea on how this can be done.
void textBox1_KeyDown(object sender, KeyEventArgs e)
{
Size textSize = System.Windows.Forms.TextRenderer.MeasureText(textBox1.Text, textBox1.Font, textBox1.Size, TextFormatFlags.Default);
if(textSize.Width >= textBox1.Width)
{
textBox2.Focus();
}
}