Hi, maybe I can help you as we went many times in Mongolia. you can across border from Russia to Mongolia on west on Tashanta city. point is open for foreigners every day +/- 9-16AM except on Sunday. it's possible as this happen for Chinese border in Zamid uud-erlian you might be oblige to across by vehicule. in that case you will find a taxi to put your bicycle inside and across border or will ask to someone who is crossing to pick you just to across border. then you will continue for Olgy who is nice small town where you can find some guest houses and hotels and a lovely museum.
as you can understand until UB not so much asphalt only maybe average 200km-300 according the direction you will choose. running track are worse but you will forgot this in front of marvellous landscape and hospitality given by nomads you will meet.
if you wish to have more advice, contact, ideas, just drop some lines.
have nice trip
PS be careful as May nights are still cold, take a good sleeping bag with you, you can buy also a dell (mongolian coat) who is perfect for Mongolian climate, cost +/- 60$ on market