I picked up a 500W inverter from Walmart (I think) about 5 years ago and have been using that. It has 2 120V plugs and it works perfectly with my laptop (probably overkill).
Since your laptop has a main battery, that should act as a sufficient filter if there's any irregularities in your inverter output. But since you are also plugging in a bridge, you won't have that layer of protection on that. But I don't think it will be an issue.
I'm not sure about the WRT45GL but you could be our guinea pig! Let us know how well it works out.
For I am not ashamed of the gospel of Christ: for it is the power of God unto salvation to every one that believeth