No, that can't be it.
SEROUT and SEROUT2 are bitbanged routines so they don't use the (E)USART and therefor not the TXREG. HSEROUT does use the (E)USART but its smart enough to pace itself as to not overwrite TXREG.

The receive buffer in the Bluetooth module on the other hand...what if you split the string and send it two chunks with some delay in between?