Can anyone here provide information on likely travel routes from Jerusalem, or Antioch, to the Persian gulf, during the crusades? Links or maps would be greatly appreciated, if possible.
Your best bet is here. Uncheck the Roman things, expand the Medieval menu, expand Crusades, and you can choose which routes you'd like to see.
For more general information on traveling within medieval Europe, see the maps in Michael McCormick, Origins of the European Economy (2001). For more specifics on travel within the Mediterranean, also including maps, see Peregrine Horden and Nicholas Purcell, The Corrupting Sea (2000). Both suggest that journeys were often made by short stages, generally staying within close sight of land (although it's hard to get out of sight of land in the Mediterranean). These sources tend to focus a little earlier than the Crusader period, but both also include general discussion about changes throughout the middle ages.
For the Persian Gulf, I'd recommend reading up on the Belitung shipwreck, which was an Arabic trading vessel around 800. It was built in Oman or Yemen of wood from East Africa, repaired with parts in India, picked up a cargo of fine porcelain in China, and then sunk in the shallow ocean sailing south into Indonesia. It's afterlife is just as interesting, and it's now on display at Universal Studios Singapore. I'd recommend starting with the bottom citation (which is freely accessible), but I've included the rest for reference.
Michael Flecker, "A Ninth-Century AD Arab or Indian Shipwreck in Indonesia: First Evidence for Direct Trade with China," World Archaeology 32.3 (2001): 335-54.
Michael Flecker, "A 9th-century Arab or Indian shipwreck in Indonesian Waters: Addendum," International Journal of Nautical Archaeology 37.2 (2008): 384-86.
Pauline Burger et al., "The 9th-Century-AD Belitung Wreck, Indonesia: analysis of a resin lump," International Journal of Nautical Archaeology 39.2 (2010): 383-86.
Michael Flecker, "A Ninth-Century Arab Shipwreck in Indonesia: The First Archaeological Evidence of Direct Trade with China," in Regina Krahl et al., eds., Shipwrecked: Tang Treasures and Monsoon Winds (Washington DC: Smithsonian, 2010), 101-19.
I second the McCormick's book that /u/textandtrowel mentions is quite good. It has an appendix that compiles all the examples of movement on the Mediterranean in the 7th-early 9th centuries. Horden and Purcell is a little more...theoretical.
If you want more primary documents, check out the Rihla of Ibn Battutah and the Ross Dunn companion piece, The Adventures of Ibn Battutah. You can also browse the texts of the Palestine Pilgrims Text Society online: https://archive.org/details/libraryofpalesti01paleuoft.