Disclaimer: this is mostly personal experience, and quite outdated (2015).

It depends a lot on how you define "safe" (for example, would you feel safe talking to a border guard threatening you in attempt to squeeze a bribe, but without involving physical violence?), but generally your safest route would be through Europe, Russia and China. Then you have a few choices, none of which is hassle-free:

- China - Nepal (via Tibet) - India. This will require, besides a Chinese visa, a special permit for Tibet. According to a few agencies I talked to in Feb 2016, the permit required you to join an organized tour and stay with your group. Path to Lhasa would be reasonably easy (there is a train), but from Lhasa to Kathmandu you would have to hire a car - again, as part of your tour. Once you get to Nepal, from Kathmandu you can catch a direct bus to India, even all the way to New Delhi (although I'd recommend to take a bus to the border, and catch another one at the other side - it is much faster, and also cheaper).

   You may hear stories about people crossing to India directly from China through Nathu La, but as far as I know, it is not opened for non-piligrim visitors.

- China - [Laos - Thailand] - Myanmar (Burma) - India. Lots of paperwork. According to Myanmar authorities (Oct 2015), Myanmar-India overland border crossings were opened to foreigners. However they require special permits from both countries (i.e. to cross overland from Myanmar to India you need to get special permits - besides your visa - from Myanmar and India). This is very unreliable route. Situation in Myanmar regarding overland crossings changes often, and you're not guaranteed to be able to continue into the country once you cross the border. For example, at Tachilek crossing you can get in (from Thailand), but cannot travel far through overland, although you can fly from Tachilek airport via domestic flight. This way you also end up in the restricted areas of India, quite far away from Delhi.

- Routes via Iran and Pakistan, or through Bangladesh are also possible but less safe. Unless you have been to, and feel comfortable in strict Islamic countries - and this includes covering up yourself - I would strongly advise against this route for a solo woman. For a mixed couple or a man those would be reasonably safe though.

- Above I see someone mentioning Tajikistan, but I don't think there is a route there which does not involve Khyber pass in Afganistan (and crossing Pakistan too), and this is not considered safe for foreigners.

Now regarding the countries in your route:

- Russia is relatively safe if you're taking trains using a cheaper "platskart" class (the "coupe" class has a compartment for 4 with locked doors, and if you end up with three males who enjoy drinking, it might not be so safe).

- China is safe, and this includes Tibet.

- Nepal is safe. Natural dangers such as earthquake are higher risk there.

I'd say among those three you'll have higher risk of harassment in India itself.