The only 'invitation' needed in the process of visiting Russia, is the Invitation when applying for a Visa for yourself - assuming your home Citizenship requires a Visa.
Once you have a Visa you can go. All you need is your Passport. If riding/driving the minimum documentation you NEED is:-
Driving Licence - original
International Driving Permit - it includes a page in Russian. Google 'International Driving Permit' for details.
Registration Document for vehicle - original. With Letter of Authority from Registered Owner/Keeper if not yourself.
Insurance certificate issued by a Russian company - obtainable at borders prior to entering. Cost me £32 for 3 months on a motorbike. This is necessary irrespective of cover provided by your own insurance. Police and Border checks only recognise a Russian insurance certificate.
100-200 Roubles (about £2-£4) in cash for the Temporary Import Certificate they will issue, that you will have to carry with the vehicle. This is recognised by Police as a local Registration Document.
On entry you also receive a Migration Card and should use this with your Passport to get Registration within 3 working days, at any addresses you stay at.
In Russia -
- ALWAYS carry on your person your Passport, Migration Card and Registration.
- ALWAYS have with you, if out with the vehicle, the Temporary Import Cert, Driving Licence, International Driving Permit, and Russian Insurance Cert. These will satisfy the many DPS (Road Police) stops you will encounter - happens to all roadusers, Russian or foreign, especially if on a bike.