All depends on the rules of canton of residence. Concerning the possible home office deductions you can find more information here https://treuhand-suche.ch/forum/d/306-home-office-expenses-may-i-deduct-them
But I do not think that it is your situation. In cantons like Zurich or Zug you can deduct travel expenses, meal costs etc. for the entire year regardless measures to combat the Covid-19 pandemic. It means that you cannot deduct your home office expenses for 3 months, but check your cantonal rules for sure.
Regarding your question about transport expenses. Deduction for using someone else's car for commuting to work is possible and limited to CHF 3,000 for direct federal tax. You have to check the cantonal limit separately. Basically it makes no sense to combine the deduction for bike commuting with the deduction for car commuting. I think you reach these federal and cantonal limits without the bike.
People treat New Years like some sort of life-changing events. If your life was boring last year, it’s probably still going to be boring tomorrow. However, not in your case. 😁
All the best,