For that, you can basically buy a plane ticket to Riga (Latvia) by Air Baltic or any cheaper one buy a bus ticket from Riga to Tallinn for starting from 5 Euro.
Beside that, you don't even have to go Estonia to create the e-citizenship, create a bank account etc.
The company leapin handles anything for you including creating the bank account etc.: Plans & Pricing | LeapIN
The bank Holvi (which fees you €35 a month) also lets to create your account online and they serve you free e-billing service and e-accounting. For for Holvi, you should find an address in Estonia and handle the accounting/taxing stuff yourself.
PS: But as far as I know, Holvi does not support SWIFT money transfer, you need to be in the Euro zone in order to use it.