Bolshoi tickets in advance

To buy tickets
https://www.bolshoi.ru/en/timetable/
I’m not completely sure if there’ll be performances in May. In general, theaters go on tours in summer.

If you’re interested in the venue, go to this page for the building tours
https://www.bolshoi.ru/en/visit/excursions/

Some performances for May have just been announced. Tickets are not on sale yet, but the site (as listed above by shinkasen) says "soon on sale" for most dates.

To buy a ticket online, you'll need to register on the site with your email address, as described here. They will send an email with your password, which you can then use to log in and buy tickets. The first email address that I tried didn't work - I did not receive the password email, including in my spam folder. A gmail address worked perfectly.

You can review this Bolshoi Theater Seating Plan which shows 9 colored seating zones and the expected visibility for each, even down to certain seats. Decide your price/visibility preference, choose your seats and book!

https://www.bolshoi.ru/en/visit/schema/

Note: tickets on alternate sites (such as Bolshoi Moscow) are significantly higher priced (by many hundreds of dollars) for dates I've compared for April.

We were in Moscow in April a few years ago. We simply went to the main ticket office and using our Google translate app were able to purchase last minute tickets for that night. The seats weren’t great, but it was wonderful to experience the Bolshoi. You might have to sit separately, but we lucked out and got 2 together. My memory is that we got the tickets for about $20 each.

Having just purchased tickets to the Bolshoi ballet for a performance in May, I will add a note regarding helpful information on this page:
https://www.bolshoi.ru/en/visit/buyingnew/

About 1/3 of the way down the page, beneath the Ticket Sale Policies and a note about children aged ten and younger, are links of the format:

"Schedule of Preliminary Ticket Sale for [MonthName] 2020"

These links show a schedule of when the tickets will go on sale for each performance in that Month for 3 ticket types:
(1) Ticket sales at the box office to named passport holders
(2) Ticket sales on the website to named passport holders
(3) Ticket sales that do not specify a named passport holder ("e-tickets")

For May and June, 2020 ticket sales, I am seeing:
Ticket type (1) and (2) go on sale at Noon, Moscow time on the date indicated for the show
Ticket type (3) go on sale 6 days later at 11am, Moscow time

The tickets I purchased went on sale at exactly the scheduled time.

The "advance" Ticket sales of type (1) and (2) to named passport holders result in a "certificate" which must be exchanged in person at the box office, at least 1 hour before the show, by showing the passport and the credit card used for purchase.
https://www.bolshoi.ru/en/visit/buyingnew/2/

Ticket sales of type (3) are "e-tickets" and do "not require to be exchanged [for] a regular ticket."

Our trip to Moscow is looking less and less likely. Bolshoi performances through April 10th have been cancelled. The Bolshoi website says that, for tickets purchased online via credit card, full refunds will be issued via the same card. (Although I should mention that the "full refund" might not look so "full" when it goes through the latest exchange rate. With the value of the ruble falling dramatically, it won't buy back as many dollars as we used to purchase our tickets.)

One small consolation is that the Mariinsky in St Petersburg (whose performances are also on hold, currently through March 31) is broadcasting ballet performances via webcast:

https://mariinsky.tv/e

For example, their March 20th is an archive performance of Cinderella!

Bolshoi performances have now been cancelled through April 30th. They are streaming free broadcasts of various ballets, each available for 24 hours.

Available today is the ballet Marco Spada from the Bolshoi:
https://www.youtube.com/watch?v=C-0ZfKcB-Xw