To answer this question, one must first understand that Bitcoin is always traded for something. Money doesn't go "into" Bitcoin, it just changes hands between private parties. If I have 10 BTC and you have $60, and we decide to trade, you now have the 10BTC and I have $60.
You could examine the volume of trades on exchanges; trade volume would give you some idea how much Bitcoin is changing hands. The exchange only facilitates the trades, so it is still a person-to-person trading that is happening when you buy bitcoins, as described above. However, Bitcoin can also buy goods and services, and can be traded without using centralized exchanges, so the actual economy of Bitcoin is bigger and is hard to measure. The Bitcoin protocol also hides how much money is actually changing hands, you can't look at how much money is being sent on the Bitcoin network to answer how large the economy is. A lot of the transaction amounts seen on the network are the client sending money back to itself, and these can't be distinguished from purchases. Also, Bitcoin trades don't even need to go out on the network if they are taking place between customers of a "Bitcoin bank" (or even a gambling site), where bitcoin balances of customers only change within the site's accounting system.
Some might say that deposits and withdrawls of funds into exchanges might be what you are asking, how much is being deposited by people to buy Bitcoins. However, this isn't an answer to your question either. If I deposit $1000 to my MtGox exchange account, that money hasn't "gone into Bitcoin", it is just waiting for me to use it for trades as described above.
The current value of Bitcoin on exchanges also doesn't indicate money flow or the real value of all Bitcoins. Exchange values are the meeting price of just a few buy and sell offers. Prices can change without any bitcoins changing hands - if everyone decides not to sell for less than $10, than the price of Bitcoin became $10 without any being traded. If eight million bitcoins currently exist, and you want them all for yourself, you will have to pay much more than the current $6 per Bitcoin to buy them all.
The only way one could use the phrase "money going into Bitcoin" is when considering mining. Mining Bitcoins creates wealth, like finding a gold nugget in a river bed. Every day, about 7200 new Bitcoins are mined, and they obviously have value. Many of these are sold for cash to new investors in Bitcoin or used to buy goods or services, but many are being held as an investment. You would need to survey every miner and find out how many newly-minted or never-spent bitcoins they sold and determine the value of government currencies, goods, and services the "free" bitcoins bought them to arrive at how much money is going into Bitcoin.