Assuming both your router (and hers) will accept external antenna's... and have some sort of bridging capability... it is pretty easy to do.
The problem is staying under your budget.
You will need an antennae on each end (facing each other).
Omni's probably won't have enough boost to work at 300 feet, or at least not with max signal strength.
Directional antenna's - either buy some... or build your own. It is easy to build some Yagi style antenna's... cheap, and work very well
Cheapest one I know of, and it works: http://www.instructables.com/id/10--WIFI-16dBi-Super-Antenna-Pictorial/step7/results16dBi-antenna-picks-up-21-aps-instead-of-7-/
Not the best for outdoor mounting though!
Lots of ideas here: https://www.google.com/search?q=build+your+own+yagi+antenna+for+wifi&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a&channel=sb
More good info here: https://www.google.com/search?q=directional+wifi+antenna&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a&channel=sb
Amazon, Ebay, etc.. have a lot of inexpensive Yagis also.. http://www.amazon.com/s/ref=nb_sb_noss_2?url=search-alias%3Daps&field-keywords=yagi
You can find some better gear and lots of connecters and adapters at: http://www.l-com.com/
CDW and Radioshack also have a decent selection of parts and stuff... for getting it all working.
The antenna's are the easy part. Making sure that your routers can handle it.. that is the main thing (that and good line of sight for the antenna's) . A good signal strength meter can help with the antenna alignment... but you can get by without one if you play with it.
If you need help with it... please list router makes and models, with firmware revisions also.