NMR relaxation can be described with two related parameters, relaxation rate (R2) and relaxation time constant (T2), They are simply inverse of each other. Fast T2 relaxation means lower T2 time constant and low water mobility usually in bound water. Think of it as if water is bound to macro-molecule, water mobility is now tied to macro-molecule mobility which is slower than free water mobility. For T2 relaxation it usually means faster relaxation (R2) and lower T2 time constant. For list of T2 relaxation mechanisms please see MRI-questions.

For your experiment however, if the bound water and free water protons are exchanged faster on NMR time-scale they both will give rise to one weighted average relaxation rate. If the exchange is slow on NMR-scale you may be able to differentiate bound water R2 from free water R2.   

http://www.mriquestions.com/causes-of-relaxation.html

https://www.ncbi.nlm.nih.gov/pubmed/25788228

Compact NMR relaxometry of human blood and blood components