The TRMT bit (TXSTA.1) reads 0 (TSR full) while the USART is still shifting out data.
Wait for it to go to 1 (TSR empty) before switching back to receive mode.
Code:
TRMT   VAR TXSTA.1

HIGH RE_DE
HSEROUT ["Hello World!"]
WHILE NOT TRMT : WEND
LOW RE_DE
Be sure to have "Fail-Safe" resistors that bias the network to "True Idle" levels.