The time it takes for bed bugs to die without a host will depend on the temperature and humidity of the area or room they're in.
It typically takes between 20 to 400 days for the bed bugs without a host to die.
The higher the temperature and humidity the less time it takes for the bed bugs to die so it's a good idea to have a heat treatment done to kill off the bed bugs in your home.
If the temperature is colder then it can take up to 400 days for the bed bugs to die without a host which is over a year.
I would highly recommend having an exterminator come into your home and do a heat treatment and pay for the cost of it because although bed bug home remedies do sometimes work it's best to use an exterminator who has the best equipment to get rid of and kill off the bed bugs.