With many thanks to Bentley's Rudi Wells for this tip!

To place text on an element without breaking the elements, set the placement method to Above Element, and the Line Spacing value to negative 1/2 the text height as shown in the graphic below.

This technique is not supported in MicroStation V8i or MicroStation V7.

V8 - Drive the line spacing value with this keyin:
mdl keyin calculat;calc tcb->textStyle.lineSpacing=tcb->textStyle.height/-2