Schiff's concern that Russia was helping Trump to win so that Putin could get a foreign policy favorable to Russia fits within the role of a ranking member of the intelligence committee. Schiff simply pointed to the facts below, which we all can see, to explain his basis for suspecting there was collusion.
I recall that Trump was reading hacked documents from the DNC during his campaign, and that Roger Stone, an associate of Trump, had indicated he had inside knowledge of what was going to be released through WikiLeaks.
Also, The Mueller report found that during the 2016 election, Paul Manafort was sending polling data to Konstantin Kilimnik, who was known to have connections with Russian intelligence. In addition, three independent reports found that Russian operatives were extensively using social media platforms, posing as Americans to amplify propaganda meant to damage Hillary.
Trump openly spoke of changing US foreign policy concerning Ukraine and Crimea during his campaign. He can even be seen asking Russia to find Hillary's emails. After becoming President, he was seen in Helsinki conveying that he trusted Putin over American intelligence agencies.
The Trump campaign met with the Russians in June of 2016. Two months later when Don junior was asked what he thought about the suggestion that Russia had hacked the DNC to help Trump win, Don jr. scoffed, declaring it to be fabricated lies by the Hillary campaign. One year later we all saw Don junior admit that the Trump campaign had met with Russians to discuss obtaining dirt on Hillary. The emails to Don Junior were even made publicly available, which state that Russia wanted Trump to win. The Trump campaign knew that Russia wanted to help them win, yet they claimed it was a hoax.