Why investing in bonds imply a decrease in money demand? In the description of so-called money market, we have demand,Md, for liquid money from individuals (and firms) and supply,Ms, of liquid money, likely from central banks. Now it is assumed that if interest rate,r, would increase, the demand for money,Md, would decrease due to people's preference of bonds(or other high yield securities) over money at high interest rate. 

This doesn't make sense; whereas it is true that "households" would buy bonds in exchange for money at higher r, bonds are simply transfers of money, from households to firms or governments. So the aggregate money in the economy remains constant, as firms/governments would utilize the bonds' money in the economy. Thus, if we consider the economy as a whole, the "demand" for money does not change with people opting for bonds.

If we only consider the households' demand for money, then the analysis in money theory and LM curve would be inaccurate; In the discussion of LM curve, we have MV=PY and M/P =Md(Y,r). M/P essentially denote the "real money" supply from central bank. In the first formula MV=PY derived from money theory, If M/P hold constant, Y, also known as the aggregate income, is also constant; This is consistent if we consider the economy as a whole. However, in the second formula, It is understood that the money demand Md(Y,r) account for only the "households". It is unreasonable to discuss the dynamic between money supply and money demand when we have the whole economy in consideration on one hand and have only a sector of the economy weighted on another hand. 

To sum up, I can understand that higher interest rate could encourage people to save up, thus effectively reduced the amount of money in circulation so reducing the "demand" but I do not see how opting for bonds decrease the demand for money unless only a sector of the economy is taken into consideration. Can someone provide some insight into this?
One thing to consider is that, when the Federal Reserve in the United States tries to manipulate the money supply, it does so through either putting more of its money into the market through bond purchases (supplying banks with money to lend) or holding money from the market through bond sales (leaving the money essentially dormant). It is not so much that bond creators receive money when people turn to bonds with higher interest rates but rather that the bonds change hands to people (households, firms, banks) who would have actually circulated money in some way if they held it in liquid form. The missing link is the central bank's money holdings.