It was one of those barriers similar to the first 200 mph mark, 250, and 300. We all remember who broke 300, who broke 200, 250?
First over 250 mph was Don Vesco in 1970 (FIM, AMA and SCTA records at 251.9xx mph on 17 September).
First over 200 mph was Wilhelm Herz (FIM, AMA and SCTA records at 210+ mph on 4 August 1956). The exact speeds are hard to pin down. Russell Wright and Johnny Allen came close, but the NSU team was the first to get there. Herz's son, Heinz, has written an excellent article (English translation published in Fast Facts, the newsletter of the Speed Record Club) on the race to 200 mph. He is also writing a book provisionally titled "Bonneville Happy Birthday 200 mph".
First over 150 mph was Joe Wright (150.74 mph - sometimes reported as 150.65 mph - on 6 November 1930). This was a big increase (13 mph) on the previous record. At least three others went over 150 mph before Rollie Free was the first to do it at Bonneville.
First over 100 mph ... you could debate this over many winter evenings, but I reckon there are at least six contenders. Different times, different rules.