Strange problem with JY-MCU (HC-06) Bluetooth module
The baud rate 57600 is a pretty marginal on an AVR (the microcontroller used) at 16 MHz, normally OK with only a bit over 2% error but some modules can be picky. The site WormFood's AVR Baud Rate Calculator shows some good tables on error percentages for various clock / baud rate combinations.

Also I just noticed  Majenko's comment and he's quite right the software serial you're using will be worse at that speed so for a start try it using a hardware UART.

That Arduino runs at 5 V logic levels so if you're not using a voltage divider to drop the transmit line to 3.3 V that might be worth try first. I've read a few mixed things about whether the HC modules are 5 V tolerant on the serial lines or not and it certainly won't do any harm trying it first to see if it resolves it.

But if neither of those steps work I'd recommend getting a USB to TTL serial converter, it seems for that module you should look for one with a 3.3 V logic level like this one for Sparkfun. They are also useful for a host of other things so are generally useful to have at your disposal.