In short (during mid-70's to early 90's):
more than 100,000,000 passengers a year (official data);
most of the flights were packed full, but sometimes quite empty;
it was very easy for a Soviet citizen to travel domestically
, the tickets were not too expensive, sometimes very cheap - the problem was rather to get them staying in 4+ hours line (personal experience; I'm sure, 4+ hours was by far not a limit). No party membership required...
It was a totally different story to travel abroad. Even to "friendly socialist" country. Enough to say, there were two kinds of passport: one ("internal" - sounds funny, passport by definition is a travel document) actually an ID
(with domicile registration, family members listed, nationality
- no, not citizenship but ethnic origin
, not even religion, ...), and another one ("foreign") for traveling abroad. You couldn't just go and order it - you had to produce documents proving you were going to travel. Then, up to early 90's, in addition to entry visa to a foreign country, you had to get "outgoing" visa
to be able to leave your
country - just having passport was not enough, you had to get a permission to leave the USSR
every time you traveled abroad (however, there were multiple "outgoing" visas too)! There were almost no "private trips", it was either a business trip or "organized tourism". To get to both groups party membership was a great advantage. As for loads, I was lucky to travel abroad like a dozen times during 1989-1992 (when it started to be way
easier, especially in Latvia), the aircraft were usually full (however, on some flights there were less than 10 people in Tu134, or about 30 people in Il86), but this was already a different era...