We are interested in the existence of expectation-driven fluctuations of a rational bubble and the (de-)stabilizing role of monetary policy. This paper highlights the key role of credit market imperfections at the household level to explain bubble fluctuations and exhibits the stabilizing power of monetary rules responding to asset prices. We consider an overlapping generations exchange economy where households realize a portfolio choice between money and a bubble. Money is held because of a partial cash-in-advance constraint affected by the size of the bubble. A higher value of the bubble reduces the need of cash, and thus increases the fraction of consumption purchased on credit. Under these credit market features, multiplicity of steady-states (global indeterminacy) and expectation-driven fluctuations (local indeterminacy) can occur for arbitrarily small market distortions. Investing the stabilizing role of monetary policy, we show that when the monetary policy rule responds only to expected inflation, a more active rule can be destabilizing by promoting local indeterminacy and has no impact on the multiplicity of steady states. In contrast to the previous policy, when the rule responds also to asset prices, then the monetary policy can be stabilizing and rule out the multiplicity of steady states.