There are many key indicators to look at to help define a bull market
Moving averages
Advances/declines
Volume
Identified support and resistance areas
Momentum indicators.
Since a bull market is one in which prices are generally rising, the basic indication of a bull market are up-sloping trend lines (and an up-sloping trend line needs to establish again since we are in free fall right now)
Additionally, price should remain above major moving averages such as the 50-day, 100-day and 200-day moving average, and the shorter-term moving averages should remain well ahead of, or above, longer-term moving averages.
In a continuing bull market, price continues to overcome resistance levels, which then become identified support levels. (We are currently in the opposite with no signals yet we are going the other way)
One sign of a solid bull market is one in which support areas are generally more solid than resistance areas, a market that, for the most part, moves higher with more ease than it moves lower. Resistance is dominant right now.
Momentum indicators like the average directional index (ADX) are used to define and confirm a bull market. The ADX is an excellent indicator for determining when the market is actually in a trend, as opposed to being in a ranging or consolidation phase.
For confirming indicators, a move in the Relative Strength Index (RSI) up out of oversold conditions is validation we could be flipping sentiment back to the bulls.
Also, beyond technical indicators, bull markets are characterized by investor confidence (which we lack right now).