Either use a text buffer in the controller, where you store the text ("Hello World!"). Then constantly translate from this text into a bitmap - either as a two-step operation or send the bitmap data directly to the diodes without storing any intermediate data.

Or use a ring-shaped bitmap buffer and directly convert any received character into bitmap data last in the bitmap ring buffer (possibly loosing the oldest bitmap data).

Whatever you do, your controller must keep track of what to display - in ASCII or bitmap form - unless you require that your PC constantly (50-100 times/second) sends out the text.