Power Consumption
A typical vanilla Duracell 'copper-top' alkaline battery has a capacity of 1000 mAh. This translates into 1.5 Watt Hours (1000 mAh * 1.5 V = 1500 mWh / 1000 = 1.5 Wh). With two batteries in serial, the voltage will go up while the capacity remains the same, so 1.5 Wh for both batteries combined.
At 550 mW, you would be able to use the vibrator for around 2.5 hours (550 mW * 2.5 h = 1375 mWh = 1.4 Wh).
An important point to consider is that cheap carbon zinc batteries only have a capacity of 500 mAh, so you had better buy high-quality batteries or, with your luck, the Meridian could run out of juice right before you come.
In the real-world, taking into account the pattern, typical usage time, discharge, etc., I reckon a 4-pack of alkaline batteries to see you through the month.