For the bike booking, I had to call the customer service once I'd bought my ticket - East Coast doesn't let you book your bike online, although that may change now it's out of Virgin's hands. West Coast does let you book online, iirc, but only if you're travelling a West Coast route (they're both called Virgin but they're different companies).
The East Coast route has been LNER (London North Eastern Railway) since earlier this year (24th June, I think) as Stagecoach (& Virgin) wanted out of the deal/were kicked out by the DfT**, so the route is now run by LNER, as an effectively nationalised railway, on behalf of the DfT. The trains and staff are the same, mind, as is the website that doesn't allow bike bookings!
For booking bikes online, I tend to use ScotRail's website, as it (still) allows the booking of bikes when booking the person. TransPennine Express and gWr's websites both also allow the booking of bikes (most of the time!) - they are both run by First Group, so the websites use the same booking engine, although unlike the ScotRail website, when they fail to book a bike, they don't tell you/fail gracefully**.
Advance tickets only become available 12 weeks before travel (normally - it can be less at weekends/bank holidays) as that is the planning window for planned maintenance on the railway - if it isn't in the working timetable by 12 weeks before, then it doesn't happen (unless it's an emergency and there is the prospect of things falling off!!)
**delete as applicable!