Which betting apps offer cycling?
This all depends on your location. If you're in Europe you have a plethora, with Betfair being potentially the largest.
If you're in North America you're more limited. Let's take Ontario, a province in Canada, for example, which recently legalized sports betting. The two main betting houses that offer cycling betting are bet365 and Betway. Others do offer cycling markets (such as BetMGM or Bwin) but their selection is usually more limited to the major races such as the Tour de France and Milan San Remo.
Certain betting houses also sometimes specialize their offerings. Betway occasionally offers 'Top 10' odds for major races and monuments, whereas bet365 generally won't. On the other hand, bet365 will often have head-to-head odds for multi-day stage races whereas Betway won't.
Betway often also covers the women's peloton and races by offering odds while the others do not. And if you haven't been watching women's races, you should, they're sometimes more exciting than the men's race.
It's worth having a few apps installed and checking them periodically. We wouldn't recommend more than a handful as you'll lose track of where you placed bets unless you're extremely diligent.