TimerOne Library - Response time
Before using libraries, try to see whether you can manipulate the timer registers directly to achieve what you want.  You may find it is easier!

In the following example I assume you are using an ATmega328 chip.  The code may be slightly different for other microcontrollers.  In that case you can read the data sheets for both microcontrollers and work out what you need to change.

I also assume the data you want to transmit is stored in a byte array.  Initialize the data how you prefer.

e.g: byte my_data[10] = {0,0,0,0,0,0,0,0,0,0};

Next, you want to initialize timer1 in the main loop

TCCR1A=0;
TCCR1B=0;


To send data at 2000 bits per second, the following settings can be used

ICR1=124; // Timer counter resets to 0 after reaching 124
OCR1A=125;
OCR1B=125; // other counter match registers must be higher than ICR1
TCCR1A=B00000010; // waveform generation mode 14, fast PWM, ICR1=top
TCCR1B=B00011011; // clock scaler 64, 1 count = 4 us.  125*4 us = 500 us
TIFR1 |= (_BV(ICF1) | _BV(OCF1A) | _BV(OCF1B)); // Clear match flags


This will set the timer1 match register bit ICF1 every 500 us.  There are several ways of using the timer to send the data.  My preference would be to poll the match flag.  The timing precision is about as good as you can get - a couple of clock cycles:

loop_until_bit_is_set(TIFR1,ICF1); // wait until TCNT1=ICR1
TIFR1 |= (_BV(ICF1) | _BV(OCF1A) | _BV(OCF1B)); // clear match flags
// switch digital output high or low depending on data bit to be sent


One way is to run a state machine loop like this:

unsigned int state;

void setup(){
state=0;
}

void loop(){
switch (state){
case 0: // idle or receiving data to be sent
TCCR1A=0;
TCCR1B=0;
// insert other code here
// conditional function, when message data received, set state=1;
break;

case 1: // setup timer
ICR1=124; // Timer counter resets to 0 after reaching 124
OCR1A=125;
OCR1B=125; // other counter match registers must be higher than ICR1
TCCR1A=B00000010; // waveform generation mode 14, fast PWM, ICR1=top
TCCR1B=B00011011; // clock scaler 64, 1 count = 4 us.  125*4 us = 500 us
TIFR1 |= (_BV(ICF1) | _BV(OCF1A) | _BV(OCF1B)); // Clear match flags
state=2;
break;

case 2:
loop_until_bit_is_set(TIFR1,ICF1); // wait until TCNT1==ICR1
TIFR1 |= (_BV(ICF1) | _BV(OCF1A) | _BV(OCF1B)); // clear match flags
// switch digital output high or low depending on data bit to be sent

// add conditional function so that when you are finished sending data, reset to state=0;
break;

}
}


As always, please upvote if you find this helpful.