It is possible to monosilylate a symmetrical diol, although this is known to be problematic occasionally.  For example, the following monosilylation was reported:
However, it turns out that this reaction is hard to repeat. If the reaction were controlled solely by thermodynamics, and if the dianion is of similar reactivity to the monoanion, then a corresponding statistical mixture of 1:2:1 disilylated:monosilylated:unsilylated diol would be expected. However, the reaction in THF is made selective by two factors: 1. kinetic deprotonation of the first anion and 2. the insolubility of the monoanion. At the initial addition of TBSCl, there is only a minor amount of monoanion in solution with the rest being in suspension. This small portion reacts and shifts the equilibrium of the monoanion to draw more into solution, thereby allowing for high yields of the mono-TBS compound to be obtained. Superior results in some cases may be obtained with butyllithium:
A third method uses a mixture of DMF and DIPEA.
Alternatively, an excess (4 eq) of the diol can be used, forcing the reaction toward monoprotection.