Most bond ETFs have switched to monthly dividends paid on the first of each month, in an attempt to standardize across the market.
For ETFs (but perhaps not bond mutual funds, as suggested in the above answer) interest does accrue in the NAV, so the price of the fund does drop on ex-date by an amount equal to the dividend paid.
A great example of this dynamic can be seen in FLOT, a bond ETF holding floating rate corporate bonds. As you can see in this screenshot, the NAV has followed a sharp up and down pattern, almost like the teeth of a saw. This is explained by interest accruing in the NAV over the course of each month, until it is paid out in a dividend, dropping the NAV sharply in one day.
The effect has been particularly pronounced recently because the floating coupon payments have increased significantly (benchmark interest rates are higher) and mark-to-market changes in credit spreads of the constituent bonds have been very muted.