score:5
There will be plenty of buses each day to Bodrum. You will find one, so long as they aren't sold out, although Sunday night is unlikely to be the busiest of travel times to Bodrum. Most will be direct, but there will be some which have another final destination.
When you arrive in Istanbul, look around for bus company offices in the district you are staying in.* They are fairly ubiquitous so you are unlikely to have to travel far to find one. Moreover, they are usually clustered around one another, which makes time and price shopping easy. That being said, they usually all leave around the same times and charge similar prices, so it won't matter much which company you take, although some are better than others.
When you buy your ticket, make sure you find out what time the service bus (in Turkish, servis) leaves from the office (usually an hour or so before the scheduled departure time). The service buses will take you to the bus station or another staging point, where you will get on the actual bus. Don't buy a ticket in Istanbul from a company without a service bus. Depending on the destination, there will be service buses to take you from the bus station to somewhere central once you arrive (in some Turkish cities, there are no service buses, but this is an exception).
Turkish buses are comfortable but they do stop every three hours or so, even in the middle of the night, so factor that into your sleep expectations.
*If you stay in Taksim, walk down to Gümüşsuyu from Taksim Square to find the offices. If you stay in Sultanahmet, walk west towards Lâleli along Divanyolu. There are offices in Sultanahmet itself, but expect higher prices there.
Upvote:3
Istanbul - Bodrum : Travel distance to Bodrum is 710 Km around 12 hrs.
Varan : 444 8 999, Daily bus at 20:30 Departing from Caglayan (Europe) and Atasehir (Asian). Service shuttles from other locations.
Ulusoy : 444 1 888, aily bus at 20:30. Departing from Merter (Europe) and Kucukyali (Asian). Service shuttles from other locations.