Mosquitos sure do bite reptiles, but generally, they do prefer to go after mammals. Mosquitos will probably opt for you and leave your tortoise or reptile . Also, mosquitos can transfer disease to tortoises, in fact, this has gotten researchers worried about the risks mosquitos have on rare tortoises.
Galapagos Islands researchers are increasingly worried about this
phenomenon due to a rise in mosquito populations: a mosquito who bites
a tourist with an infectious disease could transfer it to the local
reptile population source.
See also A New Threat to the Galapagos Tortoise: Mosquito Bites
Since your tortoise is an indoor tortoise, it's less susceptible to mosquito bites. The only thing I know of that can attract mosquitos to your tortoise would be the still water from the water dish, especially if the water isn't changed frequently. Obviously, the only solution or partial solution to this is frequent water changes.
Many reptiles will gladly make a meal out of mosquitos, so even though mosquitos can bite them,the reptile will probably eat them as they arrive.
The West Nile or EEE can be transferred to reptiles, though not as commonly as mammals. Here is a detailed pdf about the EEE including the species affected by the disease.
You don't really have much to worry about for your tortoise when it comes to mosquitos, and as shelled animals, there really is less skin for a mosquito to bite on; mosquitos would rather target you. Some other reptiles would eat the mosquitos. The only real risk here is the one in the Galapagos, since the species is endangered. You can expect some solutions for mosquito problems with outdoor tortoises when effort is put into protecting the endangered reptiles of the Galapagos.
Here are some forums and sitesfor supplementary reading:
- Mosquitoes on TortoiseForum.
- Do Mosquitos Bite Torts?
- How Harmful are Mosquitos to tortoises?