Thanks for your question. I have good news for you! Taking a bath does not typically lower your body's ability to fight infection, but if you are concerned about any specific risk factors, you should definitely discuss them with your primary care doctor
While I agree that having only a bath tub will be a bit annoying, it should not affect your health. Simply soaking your body in water will not have any effect on your immune system. The only exception to this would be if you spent so much time in soapy water that you developed breakdown of your skin. Your skin is probably the most important defense you have against infection. However, I don't think that taking a bath will put you at risk of having any skin breakdown. There are no other age groups of people that are at risk for this happening.
These types of general questions are great to bring up with your primary care doctor. There are plenty of other general health care maintenance issues you can discuss at your age. You should probably make sure that your cholesterol is checked at least once before you turn 30. In addition, you should probably have a diabetes test and have your blood pressure monitored. Other than that, as long as you are otherwise healthy you shouldn't need any more attention.