Having recently returned from a week in Corsica, I cannot advise you on any specific precautions to take from the point of view of being a solo traveller of the fairer sex. Use your judgement as you would back home and you'll be fine.
OK - there's lots to see, but there is only a small railway track between Bastia and Ajaccio (via Corte) and Bastia and Calvi (via Porto Lecce). It's very slow but scenic. Otherwise you will have to rely on buses or, I would suggest hire a car so that you can get into the beautiful interior (try Holiday Autos) and use your time wisely.
If you have a search engine on your computer, the following towns have tourist offices and they can send you lots of literature about what to see and do and how to get around - Ajaccio, Bastia, Corte, Bonifacio, Porto Vecchio, Sartène, Calvi and Ile Rousse. Or you can contact the French National Tourist Board and ask them to send you the info.
If you are travelling in the Summer period, remember that the roads are very slow going (narrow and windy) and that parking is very hard in town centres!
But it's a wonderful island. You can get there by ferry from Marseilles, Toulon, and Nice in France or Genoa, Savona, Livorno, Citavecchia in Italy.
Ferry operators include SNCM, Corsica Ferries, Moby Lines and CMN. They all have their own websites, but are a bit crazy because their catalogues don't have any prices, and you can only get these if you type in a simulation on the actual website itself!!! (That frustrated me enormously.)
There are some seasonal charters from various UK airports, notably Stansted, and a twice-weekly BA service (run by GB airways on a sub-contract) from Gatwick to Bastia. (My inlaws couldn't get over having a hot breakfast served to them!!) Bastia and Ajaccio airports have their own websites too.
Hope this gives a good starting point .... there are plenty of cyclists discovering the island, but you've got to be incredibly fit to deal with the ups and downs!