Generally, I think governments are too slow to respond to the population's demands, and they don't use enough data to make their policy decisions one way or the other, or they listen to certain corporations that give them misleading data. The relation should always be People <-> Government, not Corporations <-> Government, as it it pretty much happens in US, because of the legalized bribery that they call lobbying.
While so far our best government system is the democratic republic, and I wouldn't want a 100% direct democracy, because the danger of the "tyranny of the majority" is very real, I also think that our current governments need to become an order of magnitude more transparent and more influenced by the public.
For creating bills, I think the input process should be very open. Maybe something like the Google Moderator tool, where someone asks a question or makes a suggestion, and then others vote on it. And everyone can have their own input. You can even expand that idea and allow comments for each such suggestion, to see the contrarian views, or improvements to the original suggestion.
Basically try to crowdsource bills like this. Make a platform that crowdsources all kind of bills, and make sure as many people know about it as possible, and that it's easy to use. It wouldn't be fair if only a small part of the society could use it. Everyone should be aware about it and it should be easy to use it.
Now, this doesn't mean that the government has to necessarily implement the "winning" suggestions, but it does mean that they need to consider them seriously. In the end the representatives have to be the ultimate deciders, not the majority of "voters" there.
However, ever since SOPA almost passed in US, because they tried to pass it so quickly, just before holidays, and with as little media attention to it as possible, I've been thinking that voters should be able to veto, or at the very least postpone a certain bill before it becomes law. So let's say that if 100,000 (verified) people sign up to oppose that bill, then the bill is either vetoed for good (this idea should probably be debated more), or at least it's put through a long term process of say 6 months or a year, in which the government has to interact more with the public about it, and if the bill really is that terrible, it would give the activists more time to gather support against it.
The point of this is to stop terrible bills like SOPA, Patriot ACT, etc to pass, just because the Government says they have to pass, even if the majority of the population would disagree if they knew about it.
Representatives also need to be a lot more available to the public online, like say on Twitter, but it's probably best to put this on the same platform, and make it easy for the activists/people using it to contact their representatives directly, and get responses directly from them. I think this has the positive effect of making the representatives more responsible and more "in touch" with their voters. They should be able to get feedback and complaints directly from people like this.
This is a little off-topic, but I also think all government institutions should be using open source software, and instead of sending taxpayers' money to private companies, that may not even be from that country, the government should use the taxpayers money to further improve that open source software that everyone can benefit from in the long term. This way it would actually be the public that would see a ROI for their taxes, instead of private companies seeing that ROI.