One smart bread merchant will probably say "Hey I used to sell this for $1.50, I can do better than $100" and prices it at $90. Now everyone buys bread from him.

The other merchants feel the price pressure and the cycle continues, with the price settling down to something likely higher than $1.50 (to reflect the increased price of labor input as a result of basic income) but not so high that it totally eats the increased income.

So yes, things will cost more after basic income (after all you'd likely need some sort of inflation to find the money to give away). But in an efficient market they will not cost so much more than people are not still effectively richer than they were before. It does not change the intrinsic value of most things, it just makes certain inputs (namely labor) more expensive.